INVESTIGATION OF EFFECT OF VISUAL TREATMENT ON
ELEMENTARY SCHOOL STUDENT’S SPATIAL ABILITY AND ATTITUDE
TOWARD SPATIAL ABILITY PROBLEMS
A THESIS SUBMITTED TO
GRADUATE SCHOOL OF SOCIAL SCIENCES
OF
MIDDLE EAST TECHNICAL UNIVERSITY
BY
MAHMUT EMRE BAYRAK
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR
THE DEGREE OF MASTER OF SCIENCE
IN
THE DEPARTMENT OF
ELEMENTARY SCIENCE AND MATHEMATICS EDUCATION
SEPTEMBER 2008
Approval of the Graduate School of Social Sciences
Prof. Dr. Sencer AYATA
Director
I certify that this thesis satisfies all the requirements as a thesis for the degree of
Master of Science.
Prof. Dr. Hamide ERTEPINAR
Head of Department
This is to certify that we have read this thesis and that in our opinion it is fully
adequate, in scope and quality, as a thesis for the degree of Master of Science.
Assoc. Prof. Dr. Safure BULUT
Supervisor
Examining Committee Members
Assoc. Prof. Dr. Ahmet ARIKAN
(GAZİ UNI., SSME)
Assoc. Prof. Dr. Safure BULUT
(METU, SSME)
Assist. Prof. Dr.Erdinç ÇAKIROĞLU (METU, ESME)
Dr. Hasan KARAASLAN
(METU, CEIT)
Dr. Mine IŞIKSAL
(METU, ESME)
ii
I hereby declare that all information in this document has been obtained
presented accordance with academic rules and ethical conduct. I also declare
that, as required by these rules and conduct, I have fully cited and referenced
all material and results that are not original to this work.
Name, Last Name
: Mahmut Emre BAYRAK
Signature
:
iii
ABSTRACT
INVESTIGATION OF EFFECT OF VISUAL TREATMENT ON
ELEMENTARY SCHOOL STUDENT’S SPATIAL ABILITY AND ATTITUDE
TOWARD SPATIAL ABILITY PROBLEMS
BAYRAK, Mahmut Emre
MS, Department of Elementary Science and Mathematics Education
Supervisor: Assoc. Prof. Dr. Safure BULUT
September 2008 139 pages
The purposes of the study were to investigate the effects of visual treatment
on students’ opinion in terms of thinking process and students’ opinion in terms of
feelings in the spatial ability activities; to investigate the effects of visual
treatment on student’s spatial ability, spatial visualization and spatial orientation
The study was conducted in Ankara with 21 sixth-grade elementary school
students. One group pretest-posttest design was used. Two measuring instruments
were utilized: Spatial Ability Test and Spatial Problem Attitude Scale. Spatial
Ability Test, which was developed by Ekstrom, consists of paper folding and
surface development tests measuring the spatial visualization ability and card
rotation together with cube comparison tests measuring the spatial orientation
ability. The tests were translated into Turkish by Delialioğlu, (1996). Spatial
Problem Attitude Scale was developed by researcher. The study employed both
quantitative and qualitative research using a mixed method design. The researcher
conducted 9 interviews with nine 6th grade students from the same class. The
students were asked their opinion about the visual treatment in terms of thinking
process and feelings in the spatial ability activities. Additionally, the class was
observed during their activity time that continued 10 weeks and five hours per
week.
iv
In order to analyze the obtained data, Friedman and Wilcoxon tests as well
as one-way repeated measures Analysis of Variance were used. To analyze data
obtained from interviews, the phenomenographic method was used.
The results of the study indicated that there was a statistically significant
change in students’ spatial ability, spatial orientation and spatial visualization
scores across three time periods (pre treatment, post treatment and retention). All
three scores were significantly different from each other. Test scores were
significantly higher immediately after the visual treatment than those before the
treatment. The test scores one month later were significantly lower than those
immediately after the treatment, but significantly higher than the scores before the
treatment.
The findings suggest that visual treatment has positive effects on students’
spatial cognitive process and their attitudes toward spatial ability problems.
Selection of the appropriate visual treatment should be based on students’ needs
and their cognitive development level for providing better learning environment
Keywords: Spatial ability, spatial visualization ability, spatial orientation
ability, visual treatment.
v
ÖZ
GÖRSEL ÖĞRETİMİN İLKÖĞRETİM ÖĞRENCİSİNİN UZAMSAL
YETENEĞİNE VE UZAMSAL YETENEK PROBLEMLERİNE YÖNELİK
TUTUMUNA ETKİSİNİN İNCELENMESİ
BAYRAK, Mahmut Emre
Yüksek Lisans, İlköğretim Fen ve Matematik Alanları Eğitimi
Tez Yöneticisi: Doç.Dr. Safure BULUT
Eylül 2008, 139 Sayfa
Bu araştırmanın amacı görsel yöntemin, öğrencilerin düşünce süreçleri ve
duyguları bağlamındaki görüşleri üzerine etkisini araştırmak ve görsel yöntemin
öğrencilerin uzamsal yetenek, uzamsal görsel, uzamsal alıştırma üzerine etkilerini
araştırmaktır
Araştırma Ankara’nın bir bölge ilköğretim okuluna kayıtlı 21 altıcı sınıf
öğrencisi ile yürütülmüştür. Bir guruplu öntest-sontest araştırma deseni
kullanılmıştır. Bu araştırma için iki ölçme aracı kullanılmıştır: Uzaysal Yetenek
Testi ve Uzamsal Problem Tutum Ölçeği. Uzaysal yetenek testi Ekstrom
tarafından geliştirilmiş olan kart çevirme, küp karşılaştırma, kâğıt katlama ve
yüzey oluşturma testlerinden oluşmaktadır. İlk iki test uzaysal yeteneğin alt
boyutlarından olan uzaysal yönelim yeteneğini ölçerken son iki test uzaysal görme
yeteneğini ölçmektedir. Bu testler Türkçeye Delialioğlu tarafından çevrilmiştir
(1996). Uzamsal problem tutum ölçeği ise araştırmacı tarafından geliştirilmiştir.
Araştırmada karma metodu deseni kullanılarak nitel ve nicel araştırma yöntemleri
uygulanmıştır. Aynı sınıfta öğrenci olan altıncı sınıf öğrencileri ile 9 görüşme
gerçekleştirilmiştir. Öğrencilerden uzamsal aktivitelerdeki düşünce süreçleri ve
duyguları bağlamında görsel yöntem hakkındaki görüşleri sorulmuştur. Buna ek
olarak öğrenciler haftada 5 saat olmak üzere 10 hafta boyunca süren aktivite
zamanlarında öğrenciler sınıf ortamında gözlemlenmiştir.
vi
Elde edilen verileri analiz etmek için tek yönlü varyans analizi yöntemi,
Friedman ve Wilcoxon testleri kullanılmıştır. Öğrenciler ile gerçekleştirilen
görüşmelerden
fenomenografik
elde
edilen
yöntemle
verilerin
analizinde
karşılaştırılmış,
öğrencilerin
kategorilere
görüşleri
ayrılmış
ve
yorumlanmıştır.
Araştırmanın sonuçları göstermiştir ki öğrencilerin uzamsal yetenek, uyum
ve görsel skorlarında zamana dayalı güçlü ve anlamlı bir değişiklik bulunmuştur.
Zamana dayalı her üç skor güçlü olarak birbirlerinden farklıdır. Görsel yöntemden
sonra elde edilen test skorları, öncekilerden güçlü ve anlamlı olarak daha yüksek
bulunmuştur. Yöntemden bir ay sonra elde edilen test skorları, yöntemin hemen
arkasından elde edilen test skorlarından güçlü ve anlamlı olarak daha düşük
olmasına rağmen yöntem öncesinde elde edilen skorlardan daha yüksektir.
Ayrıca görsel yöntem öğrencilerin uzamsal zihinsel süreçlerine, uzamsal
problemlere karşı olan tutumlarında olumlu bir etkisi olduğu bulunmuştur. Daha
iyi bir öğrenme ortamının sağlanması için uygun görsel yöntemin seçimi
öğrencilerin zihinsel gelişim ve ihtiyaçlarına dayalı olmalıdır.
Anahtar Kelimeler: Uzaysal yetenek, uzaysal görme yeteneği, uzaysal
yönelim yeteneği, görsel yöntem
vii
ACKNOWLEDGEMENTS
I wish to express my gratitude to Assoc. Prof. Dr. Safure BULUT for her sincere
interest, patience and criticism throughout my study.
I wish to thank my friend Zeynep Özge DİNÇ whose love and support have gotten
me to this point.
I wish to thank Sister Emel BAYRAK for their support during my study.
I wish to thank my friend Bülent KAYA for his help during my study.
I wish to thanks my family for their patience and love.
viii
TABLE OF CONTENTS
PLAGIARISM……………………………………………………………
iii
ABSTRACT………………………………………………………………
iv
ÖZ…………………………………………...……………………………. vi
ACKNOWLEDGEMENTS………………………………………………
viii
TABLE OF CONTENTS………………………...……………………….
ix
LIST OF TABLES………………………………………………………..
xii
LIST OF FIGURES……………………………………………………..... xiv
LIST OF ABREVATIONS……………………….………………………
xv
CHAPTER
1. INTRODUCTION……………………………………………….
1.1 Main and Sub-problems of the study and Associated
Hypotheses………………………………………………………
1.1.1 Main and Sub-Problems of the Study……………………..
1
4
5
1.1.2 Hypotheses of the Second Main Problem in the Study…… 5
1.2 Definitions Of Terms………………………………………..
6
1.3 Significance of the Study……………………………………
7
2. REVIEW OF LITERATURE……………………………………
10
2.1 Theoretical Background………………………………….....
10
2.2. Definitions of Spatial Ability, Spatial Visualization and
Spatial Orientation………………………………………………
14
2.2.1. Definition of Spatial Ability………………………… 14
2.2.2. Definitions of Spatial Visualization and Spatial
Orientation…………………………………………………. 16
2.3. Studies About Spatial Ability………………………………
ix
19
2.3.1. Studies on the Importance of Spatial Ability………..
19
2.3.2. Studies on How to Develop Spatial Ability…………
23
3. METHODOLOGY………………………………………………..
29
3.1. Research Design of the Study………………………………
29
3.2. Subjects of the Study……………………………………….
30
3.3. Measuring Instruments……………………………………..
31
3.3.1. Spatial Ability Tests (SAT)…………………………. 31
3.3.2. Interview………………………………..…………… 35
3.4. Treatment …………………………………………………..
36
3.5. Procedure ………………………………………………......
43
3.6. Analyses of Data……………………………………………
44
3.7. Variables……………………………………………………
46
3.8. Assumptions and Limitations………………………………. 47
3.8.1. Assumptions………………………...........................
47
3.8.2. Limitations……………………………………..........
47
3.9. Validity of the Present Study……………………………….
48
3.9.1. Internal Validity……………………………………..
48
3.9.2. External Validity…………………………………….
50
3.9.2.1. Population Validity………………………….
50
3.9.2.2. Ecological Validity………………………….
50
4. RESULTS OF THE PRESENT STUDY………………………...
51
4.1. The results of Descriptive Statistics………………………..
51
4.2. Inferential Statistics………………………………………… 52
4.2.1. Results of Testing of the First Main Problem……….
52
4.3. The results of the second main problem……………………
60
x
4.3.1 The results of the interview related to thinking
process in the visual treatment……………………………..
4.3.2. The results of the interview related to feelings
toward the visual treatment………………………………...
60
83
4.4. Conclusions of the study……………………………………
104
5. DISCUSSION AND RECOMMANDATIONS…………………
105
5.1. Discussion of Findings………………………………………
105
5.1.1. Discussion of Findings on Students’ Thinking
Process……………………………………………………..
5.1.2. The Discussion of Findings related to Feelings
toward visual treatment…………………………………….
105
114
5.2. Implications………………………………………………….
119
REFERENCES…………………………………………………...
122
APPENDICES…………………………………………………… 128
Appendix A: Sample Questions of Spatial Ability Test…………. 130
Appendix B: Interview Questions and Purpose of Questions……
131
Appendix C: Sample Visual Treatment Activity Sheets……..…..
134
xi
LIST OF TABLES
TABLES
Table 3.1 Research design of the study……………………………………. 29
Table 3.2 Reliability Coefficients, Number of Questions, Total Scores and
the Durations for the Tests…………………………………………………
Table 4.1 Means, Standard Deviations and Maximum and Minimum
Values of the SAT, SOAT and SVAT Scores……………………………..
Table 4.2 Results of one-way repeated measures ANOVA for SAT score
with respect to time………………………………………………………...
32
51
53
Table 4.3 Pairwise Comparisons of SAT scores of students………………
54
Table 4.4 Wilcoxon signed Rank Test results for SAT scores of students...
55
Table 4.5 Results of one-way repeated measures ANOVA for SOAT
scores with respect to time…………………………………………………
56
Table 4.6 Pairwise Comparisons of SOAT scores of students…………….. 56
Table 4.7 Wilcoxon signed Rank Test results for SOAT scores of student.. 57
Table 4.8 Results of one-way repeated measures ANOVA for SVAT
scores with respect to time……...………………………………………….
Table 4.9 Pairwise Comparisons of SVAT scores of students…………….
58
59
Table 4.10 Wilcoxon signed Rank Test results for SVAT scores of student 60
Table 4.11 The Results of First Interview Questions……………………… 61
Table 4.12 The Results of Second Interview Questions…………………...
64
Table 4.13 The Results of Third Interview Questions……………………..
66
Table 4.14 The Results of Fourth Interview Questions………………........
69
Table 4.15 The Results of Fifth Interview Questions……………………...
72
Table 4.16 The Results of Sixth Interview Questions……………………..
75
xii
Table 4.17 The Results of Seventh Interview Questions…………………..
77
Table 4.18 The Results of Eight Interview Questions………………..........
81
Table 4.19 The Results of Ninth Interview Questions…………………….. 83
Table 4.20 The Results of Tenth Interview Questions…………………….. 86
Table 4.21 The Results of Eleventh Interview Questions…………………. 89
Table 4.22 The Results of Twelfth Interview Questions…………...….......
92
Table 4.23 The Results of Thirteenth Interview Questions………………..
94
Table 4.24 The Results of Fourteenth Interview Questions……………….. 97
Table 4.25 The Results of Fifteenth Interview Questions...……………….. 100
xiii
LIST OF FIGURES
FIGURES
Figure 3.1 Sample Questions of PFT………………………………………..
32
Figure 3.2 Sample Questions of SDT……………………………………….. 33
Figure 3.3 Sample Questions of CCT……………………………………….
33
Figure 3.4 Sample Questions of CRT……………………………………….
33
Figure 3.5 Students work on pentominoes activity………………………….
38
Figure 3.6 Students work on reflection activity……………………………..
39
Figure 3.7 Students work on slides, flips and turn activity………………….
40
Figure 3.8 Students work on making shapes activity……………………….. 42
xiv
LIST OF ABBREVATIONS
ABBREVATIONS
SAT
: Spatial Ability Test
SOAT
: Spatial Orientation Ability Test
SVAT
: Spatial Visualization Ability Test
SD
: Standard Deviation
M
: Mean
Df
: Degrees of Freedom
α
: Level of Significance
p
: Probability
Std. Error
: Standard Error
ANOVA
: Analysis of Variance
SPSS
: Statistical Packages for Social Science
LSD
: Least Significant Difference
CAD
: Computer Aided-Design
PFT
: Paper Folding Test
CRT
: Card Rotation Test
SDT
: Surface Development Test
CCT
: Cube Comparison Test
xv
CHAPTER 1
INTRODUCTION
Spatial ability is accepted as one of the most important intelligence type,
which is necessary for students’ achievement not only in their academic life but
also in their daily life. Since, spatial ability is crucial for students both in their
whole academic and daily lives, how to improve it has been an important issue for
people in various disciplines such as mathematics, physics, geometry, geology,
education, medicine etc (Battista, Whealthy & Talsma, 1982; Maier, 1996; Olkun,
Altun & Smith, 2005; Piburn, Reynolds & McAuliffe, 2005; Trindade, Fiolhais &
Almeida, 2002; Wanzel, Hamstra, Caminiti, Anastakis, Grober & Reznick, 2003).
Moreover, students’ opinion about treatment that aim to improve students’ spatial
ability in terms of their thinking process and feelings was another crucial issue
that should be handled by the researchers The main aim of the study were to
investigate the effects of visual treatment on students’ opinion in terms of thinking
process and students’ opinion in terms of feelings in the spatial ability activities;
to investigate the effects of visual treatment on student’s spatial ability, spatial
visualization and spatial orientation.
One of the studies that achieve to improve spatial ability by using visual
treatment was performed by Clements and Owens (1998) and Alias, Black and
Gray (2003). Clements et al. (1998) and Alias et al. (2003) stated that spatial
visualization ability was essential in effecting students’ cognitive construction and
improving their problem solving design. The use of concrete materials provided a
chance to encourage students to enhance their imagery and problem-solving
processes (Clements & Owens, 1998). Moreover, Alias, et al. (2003) believed that
great importance should be given to the concrete learning experiences before
students reach formal operation stage of thinking. In addition to this, Ben-Chaim,
Lappan and Houang (1985, 1988) found in their research that concrete experience
1
with cubes such as building; representing 3 dimensional constructs in 2dimensional drawings and evaluating them were helpful in improving students’
spatial ability.
Many studies which were different than the studies performed by using
concrete materials showed that there was a relationship between sketchingdrawing activities and spatial abilities. (Kayhan, 2005; Alias, Black & Gray,
2002; Olkun, 2003) According to Olkun, (2003) there are mainly two main
reasons for selection drawing activities. First one is it has a practical base in real
life situations and second one is concrete experience with geometrical objects are
accepted supportive in improving students' performance in spatial visualization.
Activities used in that research were divided into two groups which were
activities with concrete materials and virtual environment activities. These
activities were used to enhance students’ spatial ability. The reason for selecting
these types of activities was based on findings of similar researches. Review of
literature showed that these two types of activity helpful in enhancement of spatial
ability.
An assortment of studies maintained that spatial ability could be improved
by geometry education. Battista, Whealthy and Talsma (1982) stated that in his
research students’ spatial score were significantly higher at the end of the
semester than at the beginning after they attend to geometry course. Kausfmann,
Steinbugl, Dünser and Glück (2004) believed that using 3D dynamic geometry
provide both complete evaluation study of geometry and improve spatial ability.
In addition to this study Ives (2003) stated that using dynamic real world
geometry activities in lectures increase the number and types of external
mathematical representation used by students and dynamic models should be
included into middle school mathematics curriculum for effective teaching.
As a result of these studies, in the present study effects of geometry
education on students’ spatial ability and attitude toward spatial ability activities
were investigated.
2
Research performed by Clements and Battista, (1997) showed that using
tetrominoes and Tetris type computer game had a positive effect on spatial
competency and the ability of transform geometric shapes and get idea about the
method which is units of units of students used in both spatial and numeric
problems.
There has been a growing research base about using of virtual environment
activities to enhance spatial ability. Research results suggest that using virtual
environment activities improves students’ spatial rotation, spatial visualization as
a result spatial abilities and mathematics discoveries (Gabrielli, Rogers & Scaife,
2000; Keller, Moses & Hart, 2002; Kozhenikov & Thornton, 2006; Lisi &
Wolford 2002; Passig & Eden, 2001; Olkun, Altun & Smith, 2005; Piburn,
Reynolds & McAuliffe, 2005 Rafi, Amuar, Samad, Hayati & Mahadzır, 2005). It
was found more beneficial for students to learn through Web-based virtual
environment than usual classroom practices in the sense of improving the
subjects’ basic spatial ability (Rafi, Amuar, Samad, Hayati & Mahadzır, 2005).
Another research about improvement of spatial ability by using virtual
environment was performed by Lisi and Wolford in 2002. They claimed that
students found computer game activities enjoyable and computer-based
instructional activities could be used in schools for improving students’ spatial
ability. Additionally, on account of MBL (microcomputer-based) instruction,
students’ levels of spatial visualization increased significantly. Create isometric
drawings, transform 3-D view of objects into 2-D drawings and generate 3-D
isometric drawings from different 2-D views of geometric shapes so the spatial
visualization ability skills achieved to improve by using applet-based instructional
materials (Keller, Moses & Hart, 2002).
As a result, all these studies highlight the importance of using virtual
environment activities to improve spatial ability. Therefore virtual environment
activities were used to improve students’ spatial ability.
3
According to Battista (1994) there was a significant and positive relation
between mathematics and spatial thinking and it has often been suggested that
involvement with spatial activities can improve students’ mathematical thinking.
Guay and McDaniel, (1977) supported that this relationship among elementary
school students existed for low-level as well as high-level spatial abilities.
However, (Erbilgin, 2003; Booth & Thomas, 2000) stated that students with
higher Visio-spatial skills were better on producing different solution methods to
the problems than students with lower Visio-spatial skills. In addition to this Tatre
(1990) suggest in his research that ‘’ spatial orientation skill appears to be used in
specific and identifiable ways in the solution of mathematics problems’’ (p.227).
The way students select for solving mathematics problem depends on the
difficulty of questions. Students prefer to select visual methods to complete
difficult mathematics problems (Lowrie & Kay, 2001).
Another important aim of the study was put light to students’ opinion about
visual treatment in terms of their thinking process and feelings. There were mainly
two reasons for examining students’ attitude and their thinking process. First one
was to provide better spatial ability activities and learning environment to students
to improve their spatial ability. Second reason there was no such a study that
examine students attitude and their thinking process about spatial ability in the
literature.
Consequently, the purposes of the study were to investigate the affects of
activity-based instruction on students’ opinion about the visual treatment in terms
of thinking process and in terms of feelings in the spatial ability activities; to
investigate the effects of visual treatment on student’s spatial ability, spatial
visualization and spatial orientation. This research consisted of case studies with
6th grade elementary school students on visual treatment.
1.1. Main and Sub-Problems of the Study and Associated Hypotheses
In this section main and sub problems and hypotheses are stated.
4
1.1.1 Main and Sub-Problems of the Study
The first main problem was stated as below;
P.1. What is the effect of visual treatment on sixth grade students’ Spatial
Ability, Spatial Orientation and Spatial visualization?
1.1 Is there a statistically significant change in students’ spatial ability
scores across three time periods (pre-treatment, post treatment and retention)?
1.2. Is there a statistically significant change in students’ spatial orientation
scores across three time periods (pre-treatment, post treatment and retention)?
1.3. Is there a statistically significant change in students’ spatial
visualization scores across three time periods (pre-treatment, post treatment and
retention)?
The second main problem was stated as below;
P.2. What is sixth grade students’ opinion about the visual treatment in
terms of thinking process in the spatial ability activities and their feelings toward
the spatial ability activities?
2.1 What is the students’ opinion about the visual treatment in terms of
thinking process in the spatial ability activities?
2.2 What is the students’ opinion about the visual treatment in terms of
feelings toward the spatial ability activities?
1.1.2. Hypotheses of the Second Main Problem in the Present Study
In order to examine the first main problem following hypotheses were stated
in the null form and tested at a significance level of 0.05.
5
H0.1.1. There is no statistically significant change in students’ spatial ability
scores across three time periods (pre-treatment, post treatment and retention)?
H01.2. There is no statistically significant change in students’ spatial
orientation scores across three time periods?
H01.3. There is no statistically significant change in students’ spatial
visualization scores across three time periods?
1.2. Definition of Terms
Spatial ability: Spatial ability means mental skills concerned with
understanding, manipulating, reorganizing or interpreting relationships visually
(Caroll, 1993). In the present study spatial ability score refers to the sum of the
spatial visualization score and spatial orientation score.
Spatial orientation: Spatial orientation is the ability to visualize and
mentally manipulate spatial configurations, to maintain orientation with respect to
spatial objects, and to perceive relationships among objects in space by (Ekstrom,
1976). In the present study spatial visualization ability score refers to the sum of
card rotation test score and cube comparison test score.
Spatial visualization: Spatial visualization ability is defined as the ability to
manipulate or transform the image of spatial patterns into other arrangements
(Ekstrom, 1976). In the present study spatial visualization ability score refers to
the sum of paper folding test score and surface development test score.
Visual treatment: Visual treatment is a kind of activity based-instruction
that is performed by using different visual strategies (Chanlin, 1999). In the
present study visual treatment refers nine activities composed of manipulative
activity and virtual environment activity which promote learning spatial ability
knowledge under different education settings.
6
Cognitive domain: Cognitive domain is the knowledge speed of events
overwhelming the capacity to respond. It has three practical instructional levels
including fact, understanding, and application. The fact level is a single concept
and uses verbs like define, identify, and list. The understanding level puts two or
more concepts together. The application level puts two or more concepts together
to form something new (Piaget, 1964). In the present study cognitive domain is
the mental process that students experience while dealing with spatial ability
problems.
Feelings toward Spatial Problems: In the present study, feelings are the
emotional reactions that are given by the students when they deal and face with
spatial ability problems.
Spatial ability problems: In the present study, spatial ability problem is a
kind of problem that required mental manipulation of objects and their parts in 2D
and 3D space (Olkun, 2003).
1.3. Significance of the study
Comparisons of research findings concur that students’ spatial ability could
be enhanced by using appropriate visual treatment (Alias, Black&Gray, 2003;
Ben-Chaim, Lappan & Houang, 1985; Clements & Owens, 1998; Kayhan, 2005;
Olkun, 2003). However, students’ cognitive processes and their feelings about
activities that require spatial ability were not a common issue that was handled by
the researchers before.
Piaget (1964) determined the factors that contribute
cognitive development at the “Jean Piaget Conference on Cognitive Studies and
Curriculum Development”. These factors are psychological development, direct
experience with physical world, social transmission, and equilibration. Moreover,
Copeland (1970) stated that as cognitive development is not a passive process; it
involves acts or operations by the learner, such an environment that student acts or
mental operations on objects in physical world involve revising partial
understanding, broadening concepts and relating one idea to another. That is why
7
visual treatment was used in this research to have opinion about students’
cognitive development and feeling. This was achieved by performing interviews
with students.
Another important issue was the physical development of students. Piaget
stated that, students should reach formal operational stage (at the age of 11-12) to
understand the terms projective geometry, frame of reference, logical
classification, Euclidean geometry and space are the bases of visual treatment in
this study. Because of this reason, students selected to have opinion about their
cognitive process and feelings were at the age of 11 and 12. Understanding the
opinion of students’ about their cognitive processes and feelings in visual
treatment will provide a chance for teachers to prepare such an environment those
students can learn spatial concepts better. When teachers know which activity is
more beneficial and which activity get the attention of the students, they can
easily select appropriate visual treatment.
Studies also showed that spatial ability is also an important issue in
professional life. One of the areas which are in positive relations with spatial
ability is medicine. (Wanzel, 2003; Brandt, Davles, 2004; Keenher, 2006).
Effectiveness and safety are the most important parts of the surgical procedure.
Keenher, Lippa, Montello, Tendick and Hgarty (2006) found in their research that
3-dimesional rotation ability played an important role in complex surgical
procedure in terms of safety and effectiveness. Engineering is another important
area that is directly related to spatial ability. Most of the areas of engineering,
especially mechanical engineering, civil engineering and electric-electronic
engineering require three-dimensional thinking ability. Mechanical engineering
requires drawing different mechanical parts from different points of view while
civil engineering requires thinking the plans of buildings in three dimensions and
electric-electronic engineering requires abstract and three dimensional thinking to
construct electrical schemes (Olkun 2003).
Because of the relationship between spatial ability and other disciplines
such as mathematics, geometry, medicine, physics, chemistry and geology, a great
8
importance should be given for improving students’ spatial ability. However,
although there was a consensus about the importance of spatial ability, there were
discrepancies in application.
The new mathematics curriculum was put into
practice in Turkey in 2005. One of the main aims of the new mathematics
curriculum, which is basically founded on multiple-intelligence, was to improve
students’ spatial ability (MEB, 2005). In order to achieve this aim, a great
importance was given to spatial ability and too many related activities such as
construct cubes, perform perspective drawings, and find the open or close forms
of three prisms and pyramids were included to the new curriculum. Moreover new
curriculum gave importance to providing such an environment that students learn
by act on objects in physical world and to providing activities with respect to their
cognitive development ages. Hence, improving spatial ability and the ways to
achieve it has become one of the most important issues for educators and
curriculum developers. That is why; researcher paid attention to the activities that
aim to enhance spatial ability. Activities should be based on students’ cognitive
levels, interests, feelings and opportunities. Activities performed for this study
during 10 weeks to enhance students’ spatial ability aim to have opinion about
students’ feelings and cognitive development for better learning environment.
9
CHAPTER 2
LITERATURE REVIEW
The literature related to the present study is reviewed in this chapter. On the
basis of the content and the main objectives of the study, the literature is assorted
into two sections; definitions of spatial ability, spatial visualization and spatial
orientation, and the studies on spatial ability.
2.1. Theoretical Background.
At the conference “Jean Piaget Conference on Cognitive Studies and
Curriculum Development” held in 1964 at Cornell University, Piaget stated four
factors that contribute intellectual development. These are physiological
development, direct experience with physical world, social transmission and
equilibration. According to Piaget (1964) intellectual development involves acts
and mental operation with physical world involves relating one idea to another.
Moreover, knowledge is not copying the reality, to know something is to act on it,
to modify it or transform it which is called operation. In other words, knowledge
is something constructed by the student internally from actions he performs on
objects. That is why, teacher plays a crucial role in providing an environment that
students act with physical world and asking appropriate questions to perform
better learning.
Piaget (1953) defined logical thinking as “conscious realization of the use
one makes of a world or a concept in a process of reasoning” (p.147). Isaacs
(1965) explained the study of Piaget about logical relations in his research. The
aim of that study was to understand how children think about logical relations by
10
asking students to complete a unfinished sentence which was ended with
conjunctions such as; because, therefore, then and discordance. According to
research results the number of students’ correct answers increased with their ages.
For example boys at the age of 7 made true connection 36% of incomplete
sentences, boys at the age of 8 made true connection %50 of incomplete sentences
and boys at the age of 9 made true connection %88 of incomplete sentences. As it
understood from this study, logical thinking ability show changes with respect to
students’ ages. Piaget (1964) classified children reasoning with respect to their
ages. First stage is the pure transduction which extends to age seven, the second
stage is concrete operational stage from age seven to twelve and last stage is the
formal operational stage after the age of twelve. Just telling to think has not a
meaning for students between the ages seven and twelve. Mathematics is an
abstraction and not a part of physical world but students at concrete operational
stage are not ready for abstract level. Copeland (1970) stated that mathematics for
students at concrete operational stage should be a discovery through the physical
world with concrete objects.
The other important issue was the way of introducing geometry with
students with respect to their cognitive development. Copeland (1970) classified
geometry types as; Euclidean geometry, projective geometry, metric geometry or
measurement. Introduction with geometry starts with Euclidean geometry which
involves line segments, triangles, squares and circles. Shapes and figures are
referred to as “rigid” in shape means they don’t bend or stretch. Movement of
geometric shapes is possible but the size and shape remains the same (Copeland,
1970). However, Piaget believes that introduction of geometry should be
topological. According to Copeland (1970) mathematics of topology are not
considered rigid or fixed. Shapes may be starched or squeezed. Closed figures
such as squares, circles and triangle are the same topologically. Because, each
simple shape transform to each other by squeezing. Moreover it is also valid for
three dimensional figures. In other words cube is topologically equivalent to
sphere because cube could be squeezed from sphere. For example for a baby, face
shape of his mother changes, when his mother getting closer to him or getting
11
apart from him. Shape is not a rigid thing for him as it was described in Euclidean
geometry. Baby sees a topological structure changing in size and shape. The
transformation of shape is called homeomorphism in topology. It is also valid for
projective geometry her mother faces get different shapes with respect to position
of his mother. In projective geometry an object is not considered by itself only, it
is thought with its position in the space. Piaget (1953) summarizes” not until a
considerable time after he has mastered the topological relationships does he
develop notions of Euclidean and projective geometry” (p.75). In the conclusion
of the Piaget’s logico-mathematical model theory of cognitive development study,
topological geometry is more close to modern geometry than historical
development of it.
Cognitive development is important not only for learning geometry concepts
but also for learning spatial knowledge. According to Piaget spatial ideas
progressed at two different levels which were level of perception (as learned
through the sense of touch and seeing) and level of imagination. These two levels
follow each other. Since topological development first, topological activities
should be performed first, and then help students in abstracting familiar Euclidean
shapes have them begin with familiar objects such as ball, pencil which is the
level of perception. Finally students should begin to work with Euclidean shapes
such as squares, triangle, rectangles, and squares. The understanding of space by
the students is difficult due to the conflict between intellect and perception. Piaget
(1963) remarks that “motor activity of enormous importance for the understanding
of spatial thinking” (p.13). Level of imagination could be achieved after the level
of perception. Copeland (1970) stated that teacher asked to students define and
draw the shape which is in the student’s hand but didn’t seen by the student.
Development of spatial knowledge is directly related to understand space.
Copeland (1970) stated that vertical and horizontal axes are used to understand
objects in space in their position and relative to each other. Objects are located
above, below in relation to these axes. Locating objects relative to each other
involves both an angular and distance measurement if horizontal and vertical axes
are used as a frame of reference. Physical world provide an environment in the
12
form of vertical and horizontal axes. Students get floor as a reference of horizontal
lines and objects such as tree, wall or geometric objects as a reference of vertical
lines. However according to Piaget and Inhelder (1963) students’ understanding of
frame of reference by using vertical and horizontal lines depends on students’
stage those they in. Piaget divided stages into three with respect to students’ ages.
These stages; stage 1, stage 2 and stage 3. Piaget concludes that students need to
reach at the age of 11 or 12 to construct true conventional reference system that
students compare distances and positions simultaneously. In the Piaget’s study
students were asked to examine the picture that is rotated 180. A student at the
stage 1 is correct for only two topological relations. Students at the stage 2 three
reference points were used by the student. Student at the stage 3 model 180 model
did not cause difficulty and can be located correctly in each of 15 positions.
Piaget and Inhelder (1963) performed a study to understand child’s
conception of space. In their study students were asked to draw the shadow of the
objects inclined at various angles and rotated to various positions such as side and
end view. Pre-operational children place themselves at the object point of view, a
topological concept, dominated by egocentrism. Students at the stage 2 represent
the object as seen from their position rather than light source. For example if the
pen is located horizontally, students draw horizontal line instead of circle.
Students at operational age could easily predict the shadow of pencil by thinking
from different point of view. Kopeland (1970) concluded that projective
geometry, as far as three dimensional objects are concerned, should be performed
after the ages 11.
In conclusions, the way to introduce geometry concepts such as space,
angle, shapes (et.) to students, the way to enhance students’ spatial knowledge and
their ability to reasoning logically were directly related to students’ cognitive
development. Because of that reason, students’ cognitive development stage
should be the prior issue thought by the educators when they aim to enhance
spatial knowledge of students.
13
2.2. Definitions of Spatial Ability, Spatial Visualization and Spatial
Orientation
In this section some definitions related to spatial ability, spatial visualization
ability and spatial orientation ability will be given.
2.2.1 Definition of Spatial Ability
Although, there was a general consensus about the importance of spatial
ability in different disciplines and could be improved by using appropriate
activities, there is no definite definition of the spatial ability. Definitions of spatial
skills such spatial ability, spatial visualization and spatial orientation were given
in different discipline studies but, as it understood from review of literature,
definitions show changes. As an example, it was observed that spatial
visualization and spatial ability definitions were used instead of each other in
different studies. These are the definitions of spatial skills used in different
studies.
Lohman (1993) believed that spatial ability is crucial for high-level thinking
in science and mathematics, for the ability to produce and understand figure of
speech in language, for innovativeness in many fields and defined spatial ability
‘’as the ability to generate, retain, retrieve, and transform well-structured visual
images’’ (p.188). It is accepted by the researcher that spatial abilities are
fundamental constructs of all models of human abilities.
Another definition of spatial ability is given by Tatre in 1990. According to
Tatre ‘’spatial skills are considered to be those mental skills concerned with
understanding, manipulating, reorganizing, or interpreting relationships visually’’
(p.216). In adaptation to this definition (Carroll, 1993) define spatial ability as
‘’ability to imagine, perceives, manipulate, reorganize, and retrieve visual images
of objects or forms’’.
14
Towle (2005) stated that spatial ability is an ability that correctly imagines
three dimensional objects that are represented in two dimensions such as in
Computer-Aided Design or detailed part drawing and very beneficial skill for
engineers. Moreover, Olkun (2003) define spatial ability as the mental
manipulation of objects and their parts in 2D and 3D space.
As it understood from different studies performed related with spatial ability
it is difficult to designate the definition of spatial ability, because it is a
multidimensional skill. However a review of literature review points out that most
of the definitions draw from meta-analysis conducted by Linn and Petersen
(1985). Since the Linn and Petersen’s (1985) definition of spatial ability serve the
purpose of THIS study, it will be used. Spatial ability has been defined as skill in
"representing, transforming, generating, and recalling symbolic, nonlinguistic
information" (Linn and Petersen, 1985, p. 1482).
Visual-spatial ability defined as a visual process that understanding the 3D
information of geometric shapes concerning corner, edge, and surface relations
and transforming this knowledge into 2-dimensional drawings or imagine
(Wanzel, Hamstra, Caminiti, Anastakis, Grober & Reznick, 2003).
As it understood from review of literature review spatial ability is not a
modular concept, it consists of many spatial components such as spatial
visualization, spatial orientation and spatial perception. Thus, the evaluation of
spatial ability should be done by using several tests for a complete evaluation
(Voyer, 1995).
According to Osberg (1997) creative problem solving is depending on
combining spatial relations, classification, transformation, and rotation and
visualization activities together. Osberg (1997) defined spatial relations
comprehending the connection between objects in space that are in animated and
static environment. Additionally, he described transformation as transform an
object from one place to another without physical representation of the
transformation, he defined rotation as ability mentally rotate objects by
15
maintaining orientation and features during the process and defined visualization
as the ability to construct, manipulate and interpret images in the mind.
According to Gardner, “spatial intelligence entails a number of loosely
related capacities: the ability to recognize instances of the same element; the
ability to transform or to recognize a transformation of one element into another:
the capacity to conjure up mental imagery and then to transform that imagery; the
capacity to produce a graphic likeness of spatial information; and the like” (p. 28).
Olkun (2003) defined spatial ability as ‘’the mental manipulation of objects
and their parts in 2D and 3D space’’ (p.8).
Spatial thinking described as a mental activity which made it feasible to
generate spatial images, which were created from the sensory cognition of spatial
relationships expressed in a variety of verbal or graphical forms including
diagrams, pictures, drawings, outlines, and manipulate them in the course of
solving different practical and theoretical problem (Yakimanskaya, 1991).
Consequently, there are several definitions of the term spatial ability, in the
present study it was defined as the ability to manipulate, generate, transform,
reorganize or interpret relationships visually (Tatre, 1990).
2.2.2. Definitions of Spatial Visualization and Spatial Orientation
At the same time as examine the review of literature, it was observed that
researchers identified two main aspects of spatial ability which were spatial
visualization and spatial orientation. These are the researches that classified
spatial ability and defined it.
D Kimura (1999) defined spatial visualization as ability to recognize and
quantify the orientation changes in a scene, different than mental rotation of
objects, the estimation of one’s position in relation to a static object. Another
definition for spatial visualization was imagination ability of resulting image after
16
folding or assembling parts of an object and she describes spatial orientation as
the ability to accurately estimate changes in the orientation of an object and
testing this ability was performed by rotating 2D and 3D objects in 2D or 3D
space. Additionally, she described spatial perception as person’s ability to
determine what the prevailing horizontal and vertical directions are in a scene
where distracting patterns are present.
On the other hand, Bishop (1983) emphasized the two abilities in
visualization; First ability was interpreting figural information which includes
both reading and interpreting of the visual conventions and spatial vocabulary
used in geometric work, graphs, charts and diagrams of all types. This ability
mainly interested in the form of the stimulus materials presented. Second ability
was visual processing of the information; includes translation of non-figural data
into visual terms, manipulation of visual imagery and transformation of visual
image into another.
Linn and Petersen (1985) as a result of meta-analysis of studies on spatial
ability identified three main aspects of spatial tests, namely; spatial perception,
spatial visualization and mental rotation. Spatial perception was defined as skill to
decide spatial relationship with regards to adjustment to surroundings of their own
bodies in spite of distracting information and mental rotation as the skill to turn a
two or three dimensional figure rapidly and accurately (Linn and Petersen, 1985).
Spatial visualization was defined by Linn & Petersen (1985) ability to solve
complicated spatial ability tasks that requires multi-step manipulations.
Lohman (1979) in a review of studies on spatial ability identified two main
aspects
of
spatial
ability,
namely; spatial
orientation
and
spatial
visualization. Lohman (1979) defined spatial orientation as ability is determine
how a given object or set of objects would appear different than their original
phase from a spatial perspective and defined spatial orientation as skill require
people redirect themselves in respect to the objects in question. Spatial
visualization necessitates complex mental rotation of objects asked in mental
17
paper folding or mental rearrangement of pieces of an object to form the whole
object questions.
According to McGee (1979) spatial orientation includes the understanding
of the organization of elements within a visual stimulus pattern. Moreover, Tatre
(1990) propose that spatial orientation could be used for solving mathematics
problems in definite and particular ways and these ways include approximation
magnitude of the figure, showing mathematical relationship by adding marks,
imagining and moving shapes’ size and shape in the mind, finding the correct
answer to a problem with visual framework without any aid was provided.
Spatial visualization defined by Humphreys and Taber (1973) as the ability
to imagine the rotation of objects, the folding or unfolding of flat patterns, the
relative changes of position of objects in space. McGee (1979) extended
Humphreys & Taber’s (1973) definition of spatial visualization by adding the
skills to mentally rotate, manipulate, and twist two- and three-dimensional
objects.
Spatial orientation is defined by Humphreys and Taber’s (1973) as ability to
organize the elements in a visual stimulus pattern and stay unconfused even if the
presented spatial configuration is changed. Batista (1994) defined spatial
visualization is to understand and perform movements of objects is space and
spatial orientation is to operate the connections between the situations of objects
in space with regards to one’s own position.
Consequently there are many different definitions of spatial visualization
and spatial orientation made by researcher. In the present study, definitions of
Batista given in his research performed in 1994 were used. Batista (1994) defines
spatial visualization and spatial orientation as Battista (1994) defined spatial
visualization is imagination, comprehension and giving movement to an object in
space; and spatial orientation understanding the relations between objects’
position with regard to one’s own position.
18
2.3. Studies on Spatial Ability
In this section, studies on the importance of spatial ability, studies on how to
develop spatial ability of the students are summarized.
2.3.1. Studies on the Importance of Spatial Ability
The literature included a good deal of arguments about the possible
relationship between spatial skills and mathematics. Guay and McDaniel (1977)
investigated the relationship between mathematics achievement and spatial
abilities among elementary school children. These findings suggest that there was
a positive relationship between mathematics achievement and spatial abilities at
elementary school level students who were at different grade level and sex.
Moreover this relationship appeared to exist for low-level as well as high-level
spatial abilities. In other words high mathematics achievers have greater spatial
ability than low mathematics achievers and significant positive correlations
observed.
The other study that found positive relation that applies to the learning of
conceptual topics between spatial ability and mathematics achievement was
performed by Battista in 1994. According to Battista (1994) school mathematics
learning was performed by using near-rote memorization of procedures for
manipulating symbols that is not conceptual in nature. However, spatial thinking
and conceptual learning of mathematics are relational. Although, a girl student
with high spatial ability demonstrated poor performance in school mathematics,
she demonstrated outstanding mathematical ideas in interviews.
McGee demonstrated the difficulty of the problem proposed earlier
determining the strength and width of the field in which a spatial factor may be
found and explained that:
19
Spatial visualization seems to be required in various
perceptual-cognitive tasks involving the mental
transformation of visual images, and it has been shown to
be important for success in college mathematics, especially
geometry and algebra (Mcgee, 1979, p.899).
Another research performed by Fennema and Sherman (1977) showed that
spatial visualization was significantly correlated to mathematics achievement
closely as connected as verbal ability. These findings are also coherent with the
findings about importance of spatial visualization to mathematics learning in
general (Fennema, 1975; Sherman, 1967).
Research studies indicated that spatial ability was not also crucial for
mathematics achievement but also for problem solving ability. Study performed
by Alias, Black and Gray (2002) examined problem solving skills with engineer
students. Intend of the study was to test whether spatial visualization activities
would affect problem-solving skills in structural design. The findings suggested
that spatial visualization ability have an effect on problem solving in structural
design which is the crucial skill in guaranteeing successful design of structures in
a positive way. However, spatial visualization ability do not come into sight to
support the learning of conceptual knowledge related to bending moments, axes
and planes of references. It could be because of weaknesses in the prescribed
learning materials.
In another Tatre (1990) study, fifty-seven tenth-grade students who scored
high or low on a spatial orientation test were used to understand the effect of
spatial orientation skill in the solution of mathematics problems. Research results
showed that spatial orientation skills were beneficial in specific and identifiable
ways in the solution of mathematics problems. These ways include approximation
magnitude of the figure, showing mathematical relationship by adding marks,
imagining and moving shapes’ size and shape in the mind, finding the correct
answer to a problem with visual framework without any aid was provided.
Additionally, Booth and Thomas (2000) performed another study related
with problem solving ability. In his study a group of students with mathematics
20
difficulties were divided into two groups in terms of their visuo-spatial abilities.
Arithmetic word problems were given students to solve in three different
presentations: orally; with a picture; and with a diagram during an interview. The
results show that the high visuo-spatial skill group performed significantly better
on these problems than low visuo-spatial skill group.
In addition to these studies, it was maintained by researchers that there was
a relationship between logical thinking ability and spatial ability. The study of
Kayhan (2005) could be given as an example. The purpose of the study performed
by Kayhan (2005) to investigate the relationship between mathematics
achievement, logical thinking ability and spatial ability with 9th grade high school
students from three different schools. After the study significant positive
relationship found relationship between mathematics achievement, logical
thinking ability and spatial ability.
In other study effects of spatial ability in promoting the logical thinking
abilities of students with regard to programming language was investigated by Tai
in 2003. The study showed that students with high spatial ability were better in
logical thinking ability and computer programming than students with low spatial
ability. Moreover those students had positive attitudes towards Computer-Assisted
Learning (Tai, 2003).
A study was conducted by Hodgson (1996) with the university students to
investigate the use of Venn diagrams to visualize set expressions. The results of
the study showed that the
Translation of set expressions provided a rich content for
studying students’ formation and use of procedures, their
understanding and operationalization of set operations, and
their ability to establish connections between alternative
representations of mathematical concepts (Hodgson, 1996,
p.176).
In another study performed by Erbilgin (2003) four 8th grade students were
interviewed to understand the effects of achievement and spatial visualization on
21
students’ use of multiple with respect to the concept of linear functions. The high
spatial ability students were better at pattern finding and producing different
solution, demonstrated a deeper understanding of the concept (linear equations)
and each representation whereas the low achieving-low spatial ability student had
the weakest understanding of the concept of linear equations among the four
students.
Furthermore, Brandt and Davles (2004) performed another study about
initial learning of a spatially complex surgical technical skill. The aim of the study
was to examine correlation between Mental Rotation Test and performance of a
spatially complex surgical skill. Research results showed that mentally rotation
ability an object in 3 dimensions has a crucial role on initial learning of a spatially
complex surgical technical skill. Surgical residency training and maintaining a
progressive surgical practice could be achieved by improving spatial ability and
increasing proficiency in learning surgical techniques. In addition to this it was
found that in the research self-directed- learning was as effective as and more
useful than traditional lecture-based learning.
A study was conducted by Ferk and Vratacnic (2003) with the primary,
secondary and university students to determine the meanings different kinds of
molecular structure representations used in chemistry teaching showed that spatial
ability was also important for chemistry teaching. The results of the study showed
that using 3D molecular models are the best way to introduce the topics about
molecular structure for primary school teachers. Moreover it was suggested in the
study that an opportunity should be given to students to construct 3D molecules
and manipulate them in 3D with the use of mirrors. Another important point
derived from study was the importance of guidance to draw students’ 3D
observations in two dimensions by using molecular models and the overhead
projector for an effective teaching.
22
2.3.2. Studies on How to Develop Spatial Ability
A lot of research performed about improving spatial ability insisted that,
there was a positive relationship between spatial training and the students’ spatial
skill enhancement (Herskowitz, Parzysz & Van Dormolen, 1996; Olkun, 2003;
Osberg, 1997; Owens & Clements, 1998; Pallascio, Allaire & Mongeau, 1993).
In the study carried out by Gabrelli et al. (2000) Virtual Reality was
investigated. The main goal of the study was to explain, how 6 years old children’
performance was affected by a different type of virtual reality scene activities.
Virtual reality technology provides a chance to design 3D worlds and navigation
activities that have many similarities with occupations we deal with in the real
world. The outcomes of the study exhibited that children were capable of
developing and displaying different levels of allocentric knowledge about the
virtual world depending on the way they had familiarized with it and on the
characteristics of the task demands. Memory of objects' location in the virtual
scene and the analysis of their way finding abilities within the scene were used to
measure children's knowledge of the spatial layout of the environment. This
finding contributes to enlighten the design of virtual reality technologies intended
at supporting or evaluating spatial abilities in children at the age of six (Gabrielli,
Rogers & Scaife, 2000).
Another study was carried out by Olkun (2003). In his study the effect of the
engineering drawing application on spatial ability was investigated. The aim of
the study was to provide activities for improving middle grade students’ spatial
ability with engineering drawing applications. There were mainly two reasons for
choosing engineering drawings in this study. First one was drawing conventions
are required in man technical occupations and engineering drawing has a practical
base in real life situations. Second reason was concrete experience with
geometrical objects were proved as a helpful in improving students' performance
in spatial visualization. Research results exhibited that spatial ability is important
and could be improve through engineering drawing activities (Olkun, 2003).
23
Furthermore, the study performed by Wolford and De Lisi (2002) focuses
on the improvement of spatial visualization. In the study, pre- and post-test a
group of third grade elementary school children participated 11 separate computer
game seasons that took 30 minutes and completed a 2-dimensional Mental
Rotation test. Students in experimental group exceed students in control group in
mental rotation post-test performance but not in the pre-test. Research results
showed that there was a significant increase in students’ initial mental rotation
performance after playing computer games that lead to Mental Rotation skills.
The research results suggested that computer-based instructional activities could
be used in schools to improve children’s spatial abilities (Wolford & De Lisi,
2002).
The aim of the experiment performed by Passig and Eden et al. (2001) was
to investigate effect of rotating Virtual Reality (VR) three-dimensional (3D)
objects practicing on improving the spatial rotation thinking of deaf and hard ofhearing children compared to the practice of rotating two-dimensional (2D)
objects. Students were divided into two groups: an experimental group, which
included 21 deaf and hard of- hearing children, who played a VR 3D game, and a
control group of 23 deaf and hard-of hearing children, who played a similar 2D
(not VR) game research findings showed that practicing with VR 3D spatial
rotations significantly improved the children’s performance of spatial rotation,
which improved not only their ability to perform better in other intellectual skills
but also in their sign language skills.
The other study that focuses on the improvement of spatial visualization was
constructed by Keller and Moses (2002). In the study, a new instrument that was
curriculum-embedded applets for isometric drawings was developed to improve
students’ spatial visualization skills. The development process had three phases.
First, a pilot study that includes interactive software and on-line investigations
was administered to pre-service elementary teachers using an exploratory
methodology. Second, applet and investigation’s accuracy was improved and then
tested with a large number of pre-service teachers. Moreover on-line assessment
instruments were also developed in second phase. Third software is revised and
24
tested in collaboration with middle school and secondary curriculum projects. At
the end of the study students’ spatial visualization was improved. In addition to
this students were able to create isometric drawings, connect isometric drawings
with other 2-D representations of 3-D objects, and translate among these
representations. Future teachers’ pedagogical content knowledge about isometric
drawings was also improved with this study.
The study carried out by Rafi (2005) supported this claim. The aspire of the
study was to improve a group of pre-service teachers’ spatial ability understanding
for teaching Engineering Drawing for secondary school subjects. 98 pre-service
teachers who took Computer Aided-Design (CAD) course participated to the
study at Universiti Pendidikan Sultan Idris (UPSI). Participants were pre-tested at
the beginning of the semester by using mental rotation and spatial visualization
tests and then desktop WbVE was employed for five weeks in the CAD
laboratories as an instructional treatment. It was concluded that post-test of the
participants were significantly higher than their pre-test scores at the end of the
study. These results decided to use in the development of the Virtual Environment
teaching and learning prototypes for secondary school in Malaysia.
Other than studies on developing spatial ability activities Kozhevnikov and
Thormton (2006) focuses on the improvement of spatial visualization. In this
study, relationship between students’ levels of spatial visualization ability and
learning physicss in a microcomputer-based laboratory (MBL) environment was
examined. In the study, pre- and post-test a group of undergraduate students who
had taken an introductory physics course enrolled MBL instruction which
primarily used computer-based activities and manipulative aids. As a result of
MBL instruction students’ spatial visualization ability improved. Different kinds
of MBL activities that were performed by a group of science teacher were also
caused to improve students’ spatial visualization ability. The relationship between
spatial visualization and performance on the physics test was due to visual
graphical representations showed during the MBL instruction course in that
research.
25
The study performed by Piburn et al., (2005) investigated the role of
visualization in learning from computer-based images. The experiment designed
by using web-based versions of spatial visualization tests, a geospatial test, and
multimedia instructional modules built around QuickTime Virtual Reality movies.
The study results conclude that spatial ability but not spatial orientation could be
improved through computer-based instruction and engaging such activities help
students to improve intellectual skills that are crucial in learning of science and
geology. Moreover research results suggested that computer based materials could
be extensively used in preliminary laboratory courses at colleges and universities.
Alias (2002) expressed the aim of their study as to determine effect of
manipulative and
sketching
activities
on
engineering students’
spatial
visualization ability. Students were divided into two groups as treatment and
control group. Treatment group engineer students manipulated objects and gain
knowledge of sketch from observation and imagination in structural design class
while control group continued their regular structural design class. There was a
significant mean difference between students’ spatial visualization ability scores
in treatment group compared to control group. There was no difference both for
male and female engineering students about the improvement of spatial ability and
they took advantage of equally from the intervention.
In addition to this, Clements and Batista (2002) investigated the application
and improvement of spatial thinking in an instructional unit on area and motions.
Paper-pencil assessments and case studies were used to collect data and case
studies were tested as pilot with 2 third graders and 3 third-grade classrooms.
Research results showed that manipulative, papers and computer based activities
not only has strong effects on spatial abilities but also provided data to understand
students’ methods for solving the unit's spatial and spatial-numeric problems.
Degree of unitizing operation to devise spatial and numerical units and units of
units were differentiated characteristic of this strategy.
Onyancha, Towle, and Kinsey (2000) expressed the aim of their study to
examine the effect of targeted training on the spatial ability and self efficacy of
26
mechanical engineering freshmen in a college. Two different tools were
developed and evaluated in the study for using in spatial ability training. First
model was Physical Model Rotator (PMR) that provided rotation of physical
model in CAD software. Second model was Alternative View Screen (AVS) that
additionally supply a line version view of the object. Spatial ability tests were
applied to students with poor spatial ability before and after PMR and AVS
training that took for weeks to understand the efficiency of training program PMR
and AVS have proved as a system to enhance spatial ability over a short period of
time. So this system can be used to provide equality between freshman engineer
students about their spatial ability knowledge. Moreover students’ attitude toward
PMR was positive and they found system very exciting.
Chapter Summary
In summary a review of literature reveals that spatial ability is very
important not only in academic situations but also in our daily life. Researchers
discovered relationships between spatial ability and understanding geometry
concepts, chemistry, mathematics, as well as geology, medicine and engineering.
They stated that spatial ability provide occupational choices or opportunities in
professional and education life. This review has showed that students’ spatial
ability could be improved by using appropriate visual treatments. Researchers
continue to discover the best way to achieve it. Researches has shown that a
relationship exist between experience with certain spatial tasks and spatial ability
performance, and these findings indicate that enhancement of spatial ability could
be the result of variety of the activities used to achieve it.
Piaget distinguishes four main stages in the development of mental
structures; sensory-motor stage, pre-operational stage, concrete operations stage,
formal operation stage. These stages are very important in terms of understanding
the capability of students; helping educators to understand how students learn at
these ages and preparing the best learning environment. Hence, the cognitive
27
development stages are very crucial in teaching. Teachers should be aware of
students’ cognitive development and feelings when they deal with spatial ability
activities. It was difficult for the educators to search a review of literature related
to students’ opinion about their cognitive development and feelings in spatial
ability activities. The purposes of the study were to investigate the affects of
activity-based instruction on students’ opinion about the visual treatment in terms
of thinking process and in terms of feelings in the spatial ability activities; to
investigate the effects of visual treatment on student’s spatial ability, spatial
visualization and spatial orientation.
28
CHAPTER 3
METHODOLOGY
This chapter includes research design, variables, subjects, instruments,
procedure, assumptions and limitations, internal and external validity of the
present study.
3.1. Research Design of the Study
In the present study one-group pretest-posttest design was used (Fraenkel,
1996). The research design was depicted in Table 3.1
Table 3.1Research design of the study
Pre-Treatment
Measuring
Treatment
Instruments
Cube comparison
test(CCT)
Card rotation
test(CRT)
Paper folding
test(PFT)
Surface
development
test(SDT)
Visual
treatment(VT)
After treatment:
Measuring Instruments
Cube comparison
test(CCT)
Card rotation test(CRT)
Paper folding test(PFT)
Surface development
test(SDT)
29
Retention
Measuring
Instruments
Cube
comparison
test(CCT)
Card rotation
test(CRT)
Paper folding
test(PFT)
Surface
development
test(SDT)
Interview
As seen in Table 3.1, the Spatial Ability Test (SAT) was administered in the
present study. SAT was composed of four different tests which were; cube
comparison, card rotation, paper folding and surface development tests. SAT was
administered to 21 sixth grade elementary school students as a pre-test. SAT is a
paper pencil test designed to measure students’ spatial orientation ability and
spatial visualization ability. After pre-test, visual treatment that was consisted of 9
different visual activities was performed with students for 10-week period. Visual
treatment was consisted of four main activity types. These were; paper folding
activities,
computer-based
activities,
activities
with
manipulative
and
transformation geometry activities. SAT was applied to the students as post-test
after treatment. One month break without visual treatment was given to the
students and the last SAT was administered to examine retention effect. Lastly 9
students were randomly selected to interview. There were two main aims of the
interview questions. The aims were to have student’s opinion about the visual
treatment in terms of thinking process and feelings in the spatial ability activities.
3.2 Subjects of the study
The subject of the study was twenty one sixth grade elementary school
students. There were twenty one students in 6-A class in elementary school and all
students in the 6-A class attend to study. The class was regular 6th grade
mathematics class. Convenience sampling was the sampling method in this study.
This study was performed at a school in rural area.
This study is carried out in 2006-2007 education year. SAT was
administered to the twenty one sixth grade students as pre-test at the beginning of
semester and administered as post-test after the visual treatment. Moreover, SAT
was administered once more after 4 weeks later as a retention test.
Nine students were selected from 21 sixth grade elementary school students
by using random sampling. Twenty one sixth grade students’ name written on
equal size small pieces of paper and put into a bag. 9 students were selected
30
randomly from this bag. Researcher was the teacher of the students and visual
treatment had been performed by the researcher gave a chance to get detail
information about students both level of spatial ability and their behavior during
the activities. However the knowledge that accumulate from students interview
would limited. All of the students are about the ages 13-14 and none of them
repeated class 6.
3.3. Measuring Instruments
In the present study, the following measuring instruments were used;
1- Spatial Ability Test (SAT)
2. Interview
3.3.1. Spatial Ability Test (SAT):
The Spatial Ability Test (SAT) is a kind of paper-pencil test which is used
for evaluating spatial ability. Ekstrom (1976) developed the SAT and test
translated into Turkish by Delialioğlu (1996). It is composed of two sub-tests,
spatial visualization ability test and spatial orientation ability test. The SAT score
is calculated by adding these two sub-tests. The questions in each test are given in
Appendix A. Reliability; number of questions and duration are given in table 3.2.
The aim of the test was to measure students’ spatial ability knowledge. SAT was
administered to 21 6th grade elementary level students. In the present study the
reliability coefficients were given in Table 3.2. They were calculated by KR-21.
31
Table 3.2 Reliability Coefficients, Number of Questions, Total Scores and
the Durations for the Tests
SVAT
I)
II)
SOAT
I)
II)
TESTS
RELIABILITY
NUMBER OF
QUESTIONS
AND
TOTAL SCORES
PFT
SDT
0.79
0.74
20
60
12 MINUTES
6 MINUTES
CRT
CCT
0.78
0.80
160
42
6 MINUTES
6 MINUTES
DURATION
These are the sample questions SAT;
Paper folding test contains such questions; the square shaped paper on the
left side of the vertical line is folded and then a hole is made. After unfolding the
paper, which one of the shapes in the right side of the vertical line will appear?
Figure 3.1: Sample Question of PFT (Ekstrom et al., 1976)
Surface development test contains such questions; when the paper is folded
from the dotted lines, the subject on the right will be formed. By imagining the
folding of the paper, match the numbered edges to the letters. P.c. the surface
marked by X on unfolded paper on the left and on the subject on the right shows
the same surfaces.
32
Figure 3.2: Sample Question of SDT (Ekstrom et al., 1976)
Cube comparison test contains such questions; In the following cubes all the
numbers, figures and letters appears only once on each cube, but it can be in an
unseen position. Then, find out whether the cubes on the left and the right are the
same. If the cubes are the same then mark S (Same), otherwise mark D
(Different).
Figure 3.3: Sample Question of CCT (Ekstrom et al., 1976)
Card rotation test contains such questions; Find out whether the shapes on
the right side can be determined by rotating the shape on the left side of the
vertical line, in other words examine whether the shapes are the same or different.
If the shapes are the same as the shape on the left side of the vertical line then
mark S (Same), otherwise mark D (Different).
Figure 3.4: Sample Question of CRT (Ekstrom et al., 1976)
33
Spatial Orientation Ability Test
Spatial Visualization Ability Test composed of two sub-tests: Paper Folding
Test (PFT) and Surface Development Test (SDT). Reliability coefficient, number
of questions, total score of each test and duration required for each test is given in
Table 3.2. Spatial visualization ability test (SVAT) score is calculated by adding
PFT and SDT scores.
(i) Paper Folding Test (PFT): It was composed of multiple choice items that
necessitate creating mental image, folding and unfolding a piece of paper in the
mind. In the assessment of test, one point is given to each true choice. As there are
20 questions, the total score of PFT is 20. Twelve minutes were given to the
students to complete test.
(ii)Surface Development Test (SDT): It necessitates creating a mental image
of geometric shapes after folding a piece of paper, and matching items. There are
five answers to match in each questions and one point is given to each true
answer. As there are 12 questions the total score of SDT is 60. Six minutes were
given to the students to complete test.
Spatial Orientation Ability Test
Spatial Orientation Ability Test composed of two sub-tests of two sub-tests:
Card Rotation Test (CRT) and Cube Comparison Test (CCT). Number of
questions, reliability coefficient, and duration required for each test and total score
of each test is given in Table 3.2. The total spatial orientation ability test (SOAT)
score is calculated by adding CRT and CCT scores.
(iii)Card Rotation Test (CRT): the aim of the test is to evaluate the ability to
see similarities and differences between the shapes. Test composed of true-false
items. One point is given to each true answer. There are 42 questions so; the total
score of the test is 42. Six minutes were given to the students to complete test
(iv)Cube Comparison Test (CCT) : The test require to determine whether
the given two cubes that have six faces with different letters, shapes and numbers
34
are same or not. Test composed of true-false items. Each question includes 8 items
and one point is given to each true item. Since there are 20 questions the total
score is 160. Six minutes were given to the students to complete test
3.3.2 Interview
Researcher conducted interviews with nine students. The interview
questions and the purpose of them could be categorized into two parts. The first
part of the interview questions includes questions to have opinion about the visual
treatment in terms of thinking process in the spatial ability activities. The second
part of the interview questions includes questions to have opinion about the visual
treatment in terms of feelings in the spatial ability activities. Researcher wanted to
gather specific information about students’ opinion about visual treatment in
terms of cognitive process and feelings during spatial ability activities to support
inferential findings of the study. That is why interview was selected as a data
collection method. After the interview, researcher analyzed each interview by
using phenomenographic method to summarize findings about each question. A
phenomenographic analysis seeks a "description, analysis, and understanding of
experiences" (Marton, 1981, p. 180). Students’ speech was categorized with
respect to their meaning and then students’ excerpted answers were fit in these
categories. Therefore, the interview tables included the same questions for each
student. I organized the findings as follows. I made a table for each question that
includes students’ opinion about visual treatment in terms of cognitive process
and feelings. Each table was designed to have one column for each cognitive
process and feelings category. Same feelings and cognitive process of students
were settled to the same category that researcher construct in the tables. These
tables facilitated the comparison of students with each other. Moreover interview
results were analyzed by another person to provide reliability of the method.
The interviews were conducted in students’ classroom environment. The
aim of the study was explained in details for students to feel comfortable. It was
reminded to students that giving the right answer was not expected, the only
35
important thing is their opinion about the questions. It was the first time for
students to attend such an interview so they were enthusiastic and a bit nervous. A
speech was made with students about their daily life to decrease their nervousness.
A speech recorder was used to record data during interview with the
permission of students. Each interview took approximately 25-30 minutes for
each student.
As a summary, to analyze data get from interviews, the views of student
were categorized compared and commented by using phenomenographic method.
17 tables were prepared the summaries for each student. The following ones are
the sample interview questions and aim of them.
1. What did you feel when you faced with spatial ability questions for the
first time? The purpose of this question was to examine the effects of
spatial ability questions on students’ feelings.
2. In which ability you have feels change or improvement before and after
the activities in general? The purpose of this question was to understand
whether or not students put connection between spatial ability activities
and lectures.
3.4. Treatment
Visual treatment activities were applied to 21 sixth grade elementary school
students at the first semester of 2006-2007 education years. Activities were
performed five days a week and activities took 10 weeks as extra curricular
activities. Activity types were listed below; transformation geometry activity,
computer-based activity, manipulative activity and origami. In addition to them in
the mathematics courses orthographic and isometric projection, tessellations,
transformation geometry, surface area and volume of prisms were taught. So the
36
course was the part of our treatment.
The extra curricular activities were
explained below:
The first activity was pentominoes applied during the first two weeks.
Activity was performed at students’ classroom. Detailed information about the
activity was given by the researcher at the beginning. This activity was performed
for 10 lecture time and each lecture took 45 minutes. Small groups were formed
composed of four or five students by the researcher. It was explained to groups
that they were required to join parts together with at least one common side. There
were twelve parts in the set of unique parts named T, U, V, W, X, Y, Z, F, I, L, P,
and N respectively. Rules that should be followed during the activity were given
to students by the researcher. First, if one shape can be rotated to look like
another, the two shapes are not considered to be different. Second, if one shape
can be flipped to look like another, the two shapes are not considered to be
different. Each small group was given a set of sheet of activity paper by the
researcher. Students were to work together to discover all the possible ways in
which five tiles could be arranged. Shapes discovered had to be different. Students
were required to cut out discovered shapes from the squared paper and find out
which shapes could be folded into boxes. They were also asked to combine all the
discovered shapes to make a rectangle. The role of researcher was to examine
students’ work and helped students to solve their problems. Classroom
observations about students’ cognitive process and their feeling were performed
during the activities in a written form. Photographs were taken by the researcher
during the study.
37
Figure 3.5: Students work on pentominoes activity
Pentominoes activity provided good practice using the four-step problem
solving process, which includes understanding the problem, devising a plan,
carrying out a plan, and checking the work. In conclusion, this activity promoted
an atmosphere of cooperation, support the development of the problem-solving
process, supply spatial-ability skill exercises, Furthermore, and serve as concrete
representations that help ease students' understanding of abstract notions.
The second, third and fourth activities were related with spatial problem
solving with Cuisenaire Rod Patterns. Second activity was space filling activities
with rods similar in sprit to tangram puzzles. Filling activity performed for one
week, 5 lecture times and each lecture took 45 minutes. It was asked students to
fill given space on the task by using ten colors of Cuisenaire Rods. Students were
informed about the number of usage each rod. Each color rod should be used once
in each task. Approximately ten minutes were given students to complete their
task.
38
Figure 3.6: Students work on reflection activity
The third activity was rotation and reflection problems presented separately
and together in analog puzzles and sequential chains. This activity was performed
for one week, 5 lecture times and each lecture took 45 minutes. It was asked
students mainly two types of question in that activity. First one was to find the
type of rotation and reflection that would produce the resulting design in the task.
Second one was to draw the design resulting from each reflection and rotation
movement.
The fourth activity was architectural-type activities involving two
dimensional rod designs. This activity was performed for one week, 5 lecture
times and each lecture took 45 minutes. Students performed two different
activities in that part. First one was to construct the different point of views of
figures given in the task. Second one was to construct figure by looking at top,
front and side views of figure given in the task.
These three kinds of activities were performed by using Cuisenaire Rods.
The common aim of these three activities were to provide valuable spatial
problem solving experience The students need to use the rods in solving all the
problems that the concepts will have concrete foundation. Activities were
39
performed both individually and in small groups. Students were encouraged
compare and discuss their answers and problem solving strategies. Worksheets
were distributed to each student provides working space for the rods and spaces
for the answers. Students worked in groups to fill in each design with the rods
according to specifications given at the top of the page.
Figure 3.7: Students work on slides, flips and turn activity
The fifth activity was slides flips and turns. This activity was performed for
one week, 5 lecture times and each lecture took 45 minutes. The fifth activity was
divided into two parts. Part one, with its activities based on patterns of block and
white squares in 5-by-5 grids, helped students recognize-and performtranslations, reflections and rotations. Definitions of slide flip and turn were given
to the students before the activities. Students tried to shade the result-shape after
transformation movement. Part two, which involves more elaborate geometric
designs, challenges students to apply their knowledge of symmetry to finish
shading in the incomplete black-and-white patterns. There were two kinds of
symmetry in the activity which were reflective and rotational symmetry.
Reflective symmetry was in which a line drawn through the center of figure
divides it into two halves. Reflective symmetry is apparent in natural objects such
as butterflies and leaves. Students were asked to shade the symmetry of figures in
given task.
40
The sixth activity was the mirror puzzle. Mirror puzzle activity performed
for one week, 5 lecture times and each lecture took 45 minutes. It was asked
students to place a mirror on picture and asked to find given shape on the task.
How it is changed depends on where students put the mirror. In the top left hand
corner of each spread there was one design called ‘mirror master’. Mirror was
placed on mirror master to get figures on the task. In other words, aim of the
activity was to find where to place the mirror on the ‘mirror master’ so that what
you see matches each of the other designs on the task. Researcher let students to
move mirror on the ‘master mirror’ at the beginning of the activities. However it
was banned to move mirror on ‘master mirror’. Students should to think where to
put mirror before put it into practice.
The seventh activity was origami activities. Origami activity performed for
one week, 5 lecture times and each lecture took 45 minutes. Origami brings extra
meaning to a piece of paper by shaping it into a form that has symbolism.
Students were familiar to origami activities from 5th and 6th grade mathematics
class. Students were required to construct given shapes in task paper by folding
papers in a given order. Students worked as a group. Researcher focused on
modular origami because students were able to construct some basic origami
figures. odular origami consists of folding several similar and comparatively
simple shapes and fitting them all together to make a more complex construction.
The eighth activity was making shapes. This activity was performed for one
week, 5 lecture times and each lecture took 45 minutes. There were two sets of
activities which were making shape 2 and making shape 3. These two sets of
activity consisted of 10 different shapes. Each activity shape was built up out of
smaller sections. Whether students chose to complete all the sections of a model
first or add each one to the growing model as it is finished does not matter. The
models in these activities had curious properties such as rotate, fold, unfold, twist,
and fit together in unexpected ways.
41
Figure 3.8: Students work on making shapes activity
The ninth activity was Tetris computer game activity. Tetris computer game
activity was performed for one week, 5 lecture times and each lecture took 45
minutes. Tetris game activity was performed in computer laboratory and there was
one computer, in which Tetris game was installed, for each student to perform
activity. Tetris game provided three ways for students to change the position of
figures. They can move, rotate and flip the figure across a line. These are called
translation, rotation, and reflection alternately. So, Tetris was a good activity for
students to practice rotations. Tetris game activity had three difficulty levels
which were easy, medium and hard. Students performed activity at easy level in
the first two days, they performed activity at medium level in the following two
days and they performed activity at hard level last day. Students were required to
finish activity to perform new one. Students’ scores were recorded in computer
environment. The role of researcher was to deal with problems that students faced
with. Playing Tetris may help build more general visual-spatial skills and help
students get better at mentally manipulating Tetris-like shapes, and not much
more. A reasonable conclusion to draw from all this is: play Tetris is fun and it
might build some brain power.
42
3.5. Procedure
The presents study could be handled in main three headlines;
In the first part;
SAT was administrated to the 6th grade elementary school students in their
classroom environment by the researcher as pre-test. The aim of the study and
how to answer the questions were explained in details before administrated the
test. Moreover evocations were performed at the beginning of the parts of SAT.
6th grade elementary school students took visual treatment which has performed
by the researcher for 10 weeks. The activity samples performed by the students
are given in appendix C. SAT was implemented as pre treatment, post treatment
and retention to the students.
In the second part;
Besides SAT test, I performed observation of the students during 10 weekperiod in their learning environment to understand students thinking process and
their feelings about the visual treatment. I performed 10 different activities which
are Pentominoes, Tetris and tangram games, spatial ability problem solving,
translation-rotation-reflection, shading reflections, mirror puzzles, making shapes,
origami, translation geometry-tessellations, reflect it hanged mirror. Each activity
except pentominoes implemented in one week period (5 lecture-hours in total for
each activity). Observations were performed during the time students engaged
with their activities. Observations were performed during activities. Observations
could be accumulated in two types which are face to face observations and group
observations
In the third part;
The researcher has performed 9 interviews with students after the visual
treatment. Each interview took approximately 15 minutes to 30 minutes. Interview
durations show changes in respect of students’ ability to express their feelings and
thinking process. Interviews were recorded by voice recorder for better recall.
43
During the interview students were required to answer 17 questions to have
opinion about the visual treatment in terms of thinking process, attitudes toward
spatial ability problems and importance of spatial ability. Interview questions and
purpose of questions were given in appendix B. Interview questions were
prepared with respect to gaining from observations that was performed during
visual treatment.
As a summary, activities were carried out during activity lessons over a 10week period. 9 different spatial ability activities were performed with students and
almost 5 school-days were spared for each activity. Daily activities took 45
minutes. Besides activities, researcher carried out classroom observations. During
each activity hour, five of the twenty one target students were selected in both the
whole class and small group settings. Observations were performed by moving
one group to another in group working and by moving one student to another in
individual working. During the interviews, students were required to deal with
spatial ability activities. Researcher comprehended students’ methods to solve
spatial ability problems, had their feelings about the problems, and observed the
way that they applied when they faced with any kind of trouble. Notes from the
classroom observations, activity sheets that students studied in the class, were
used in the preparation of questions for the interviews and in the data analysis
process.
3.6. Analyses of the Data
The following techniques are used to analyze the data;
• Data of the present study were analyzed by using the SPSS package
program.
• Data collected from the subjects were coded by the following techniques:
- Students’ scores for each part of the SAT was transferred to
computer environment by SPSS package program
44
• Descriptive statistics were used by the following reasons:
- To get the means and standard deviations of the students’ SAT
scores.
- To find the distribution of the number and the frequencies of the
subjects.
- To detect the outliers and to check that data recording error was
made (data cleaning).
Two different tests were used to determine whether there is significant mean
difference among students with respect to their SAT scores. Repeated measure of
ANOVA was the parametric one. Freidman and Wilcoxon tests were the nonparametric one. Repeated measures ANOVA compares the means of three or
more matched groups. The term repeated measures strictly applies only when
treatments were given repeatedly to each subject, and the term randomized block
is used and when treatment is randomly assigned within each group of matched
subjects
• One-way repeated measures ANOVA was used by the following reasons:
- To determine whether there are significant mean differences among
students with respect to their SAT scores.
- To determine the differences between the dependent variables
simultaneously.
• α was set to be 0.05 as the probability of doing a Type I error
This hypothesis was also tested by using the Friedman test and Wilcoxon
test because “Use parametric and nonparametric techniques to analyze data. When
the results are consistent, interpretation will thereby be strengthened” (Fraenkel &
Wallen, 1996, p.237). Friedman Test was used by the following reasons:
45
- To determine whether there are significant median differences among
students with respect to their SAT scores.
- To determine the differences between the dependent variables
simultaneously.
• α was set to be 0.05 as the probability of doing a Type I error.
3.7. Variables
The variables of this study can be categorized in five parts. The first part
includes the variables of the first sub-problem of the study–“Is there a statistically
significant change in students’ spatial ability scores across three time periods (pretreatment, post treatment and retention)” are stated as: the pre-test, post-test and
ret-test scores of the students they got from spatial orientation
The variables for the second sub-problem of the present study –“Is there a
statistically significant change in students’ spatial orientation scores across three
time periods (pre-treatment, post treatment and retention)” are stated as: the pretest, post-test and ret-test scores of the students they got from spatial orientation
The variables for the third sub-problem of the present study –“Is there a
statistically significant change in students’ spatial visualization scores across three
time periods (pre-treatment, post treatment and retention)” are stated as: the pretest, post-test and ret-test scores of the students they got from spatial visualization
The fourth part includes the variables of the first sub-problem of the second
main problem of the study –“What is the students’ opinion about the visual
treatment in terms of thinking process in the spatial ability activities”. The
dependent variable for the first sub-problem was students’ opinion about the
visual treatment in terms of thinking process, where the interviews of the 6th
grade elementary school students are used. On the other hand the independent
variable is spatial ability activities
46
The fifth part includes the variables for the second sub-problem of second
main problem of this study -“What is the students’ opinion about the visual
treatment in terms of feelings in the spatial ability activities” The dependent
variable for the first second sub-problem was students’ opinion about the visual
treatment in terms of feelings, where the interviews of the 6th grade elementary
school students are used. On the other hand the independent variable is spatial
ability activities.
3.8. Assumptions and Limitations
In this section, assumptions and limitations of the present study are
discussed.
3.8.1. Assumptions
The main assumptions of the present study are the following:
• There was no interaction between the subjects to affect of the present
study.
• The subjects were able to understand and interpret the items truly.
• The administration of the tests was completed under standard conditions.
• All subjects answered the measuring instruments accurately and sincerely.
3.8.2. Limitations
For this study, 21 6th grade elementary school students are selected by using
convenient sampling. Visual treatment is performed with 10 spatial ability
activities for 10 weeks. 9 interviews are conducted by the researcher. One of the
assumptions is the sample size of the study. The sample may possibly not be fully
47
delegated of the population and the generalization is limited. The other limitation
was the researcher was inexperienced about making observations and
observations. To become more successful about inquiry depends on the
experience that you face with. For conquering the problem, researcher read lots of
qualitative research includes interview and observations especially their
limitations part and performed interview with students different than 9 students.
Another limitation, there was no control group in the study and therefore it does
not prove that it was the visual treatment that produced positive changes among
students’ spatial ability scores. The other limitation study was limited to subjects
at the sixth grades of the elementary schools in rural areas of Ankara during 20062007 academic years. Student’s concentration during the study is another
limitation for this study. Student’s concentration and interest to the study show
changes time to time. Students sometimes got bored about the activities. For
minimizing this effect students are awarded with spatial ability related video
games once a week. Students’ problems they face with during the activities are
talked with students and tried to find a solution their any kind of problem about
every subject. This investigation was based on self-report data, which may be
subject to bias.
3.9. Validity of the Study
In this section internal and external validity of the study is discussed.
3.9.1. Internal Validity
Internal validity of a study means that observed differences on the
dependent variable, not due to some other unintended variable (Fraenkel &
Wallen, 1996). One of the possible threats to internal validity of a study is subject
characteristics. All students attend to study were at the same grade level so the
subjects’ ages were close to each other and their socioeconomic levels were the
same. None of the students were lost during the study so; mortality effect was
48
eliminated. Another threat, which is history, was eliminated with the setting being
consistent throughout the study. The pretest and posttest, as well as the 10-week
visual treatment were administered at the same school and there was no such an
event those effect students’ responses and study procedure so; the history threat
was controlled. Administering the tests to all students almost at the same time and
same place controlled location threat. Another threat was instrumentation. To
eliminate instrument decay all instruments used were carefully examined.
Moreover, measurement instrument wasn’t altered during the study which
controls the instrumentation effect. Same data collector was used to eliminate data
collector characteristics. However, application of instruments and treatment were
not controlled by training implementers so data collector bias was not eliminated.
Another threat was because of the small sample size. “A recommended minimum
number of subjects is 100 for a descriptive study, 50 for a correlation study, and
30 in each group for experimental and causal-comparative studies” (Frankel &
Wallen, 1996, p. 111). This study began with 21 pretest subjects; none of them
were lost during the study. Such a small sample limited the ability to generalize
the results to the other sixth grade school students. Reliability or validity has been
established for SAT, SOAT and SVAT, and interview questions were coded by
two different people so; generalization of the results of this study to the overall
population was positively impacted. “Unless the instrumentation used is reliable,
meaningful relationships (perhaps causal) with other variables will not be found”
(Frankel & Wallen, 1996, p. 162). Instructor performed each activity over the
same period of time to eliminate maturation effect. There was no such a control
group that students perceive that they are receiving any sort of special attention
so; attitude of subjects eliminated In addition to this, there was no such a student
with extremely low or high scores on test so; regression to mean effect was
eliminated. Lastly, 10-week period of time was given between pretest-posttest and
one month break was given between posttest and retention to eliminate testing
effect. Last treat was implementation effect. There was no other instructor
perform treatment or by monitoring instruction so implementation effect was not
eliminated.
49
3.9.2. External Validity
External validity is extending to which the results of a study can be
generalized (Fraenkel & Wallen, 1996).
3.9.2.1. Population Validity
In the present study the sampling was convenient sampling but sample size
was small therefore the generalizations of the findings of the study were limited.
However, generalizations can be done on the subjects having the same
characteristics with the subjects of the present study which were mentioned in the
“subjects of the study” section.
3.9.2.2. Ecological Validity
Fraenkel and Wallen (1996) stated that the ecological validity is the degree
to which results of a study can be extended to other setting or conditions. The
measuring instruments were used in regular classroom settings. The study is on
sixth grade elementary school students, therefore the results of the study can be
generalized similar settings to this study.
50
CHAPTER 4
RESULTS OF THE PRESENT STUDY
The theoretical background of the study, the review of the previous studies
and the method of the present study were stated in the previous chapters. In this
chapter, analyze results conducted to get statistical evidence for our claims will be
presented. This chapter contains three sections. The first section presents the
descriptive statistics. The second section is the inferential statistics section where
the results of the testing hypotheses associated to the problems are included.
Finally, the third section of the chapter includes the conclusions derived from the
present study
4.1. The Results of Descriptive Statistics
In this section the descriptive statistics of the data are given and the row
scores are used. Table 4.1 shows the means and standard deviations, maximum
and minimum values of the variables (SAT scores, SOAT scores, and SVAT
scores)
Table 4.1 Means, Standart Deviations, Maximum and Minumum Values of SAT,
SOAT and SVAT scores
PRE
POST
RET
Test Type
SAT
SOAT
SVAT
SAT
SOAT
SVAT
SAT
SOAT
SVAT
Minimum
41
20
5
76
52
17
49
39
10
51
Maximum
105
75
30
193
132
61
156
110
57
Mean
63. 62
46. 57
17.05
119.05
89.95
29.10
91.19
67.33
23.86
SD
15.46
13.01
6.71
31.00
23.09
10.81
26.04
18.14
10.38
As it is seen in the table 4.1, mean scores of students at post-test are higher
than pre-test in all three tests. However, mean scores of students at ret-test are
lower than post-test but higher than pre-test in all three tests. These findings are
valid for minimum-maximum scores and standard deviation of scores.
4.2. Inferential Statistics
In this section, the sub-problems of the study will be examined by means of
their associated hypotheses which are in the null form and tested at a significance
level of 0.05.
4.2.1. Results of Testing of the First Main Problem
The first main problem P1: What is the effect of visual treatment on sixth
grade students’ spatial ability, spatial orientation and spatial visualization?
The first sub-problem of the first main problem is: “Is there a statistically
significant change in students’ spatial ability scores across three time periods (pretreatment, post treatment and retention)?”
For the first sub-problem the following hypotheses is stated:
H01.1 “There is no statistically significant change in students’ spatial ability
scores across three time periods (pre-treatment, post treatment and retention)?”
To test this hypothesis, one-way repeated measures ANOVA is used. One of
the main assumptions is the normality assumption. The normality assumption for
SAT is determined by Kolmogorov-Smirnov statistics. The significance values
were found .099 for PRESAT scores, .200 for POSTSAT scores and .138 for
RETSAT scores. This means that the normality assumption is satisfied because
Pallant (2001) stated that “a non-significant result (Sig value more than .05)
indicates normality” (p.58).
52
• One-way repeated measure ANOVA was used as a method. The other
assumptions for this analysis are listed below by using guidelines of Matulsky
(1999).
Effectiveness of matching: Variables are measured across three time
periods (pre-treatment, post treatment and retention). Moreover, the P value is low
(p=.000), so matching is effective.
Independence of subjects: Subjects were independent; I had 21 rows of
data obtained from 21 students. There was no duplicate measurement in each
student.
Only one factor: Research aim was to compare groups defined by one
factor which was visual treatment.
Fixed factor rather than random: This test for differences among the
means of the particular groups I have collected data from. In other words, the
factor fixed rather than random.
Gaussian assumption: Gaussian assumption is about the distribution of the
overall population of values by taking into account the scatter of data it was
understood that Gaussian assumption was satisfied.
Table 4.2 Results of one-way repeated measures ANOVA for SAT scores
with respect to time
Effect
Value
F
Sig.
Partial Eta
Squared
Observed
Power
Wilks’ lambda
.147
55.217
.000
.853
1.000
To test hypothesis, one-way repeated measures ANOVA was performed.
After testing hypothesis it was found that there was a significant effect for time
(Wilk’s lambda= .000, F (2, 19) =55,217,
p= .005). The partial eta-squared is
found as 0.85. This result suggests very large effect size by utilizing guidelines
53
proposed by Cohen (1988). To find out which pairs of time periods caused the
mean difference scores of spatial ability, least significant difference (LSD)
comparisons were used. The results were given in Table 4.3.
Table 4.3 Pairwise Comparisons of SAT scores of students
(I) time
1
2
3
(J) time
Mean
Differenc
e (I-J)
Std. Error
Sig.
2
3
1
3
1
2
-55.429
-27.571
55.429
27.857
27.571
-27.857
5.505
4.436
5.505
3.069
4.436
3.069
.000
.000
.000
.000
.000
.000
95% Confidence
Interval for
Difference
Lower
Upper
Bound
Bound
-66.911
-43.946
-36.825
-18.318
43.946
66.911
21.455
34.260
18.318
36.825
-34.260
-21.455
All three means were significantly different from each other. Mean score of
the SAT was significantly higher immediately after the visual treatment (M =
119.05, SD=31.00) than before the treatment (M = 63.62, SD=15.46). The mean
performance score one month later was significantly lower (M = 91.19,
SD=26.04) than that immediately after the treatment, but significantly higher than
the mean performance before the treatment.
This hypothesis was also tested by using the Friedman test and Wilcoxon
test because “Use parametric and nonparametric techniques to analyze data. When
the results are consistent, interpretation will thereby be strengthened” (Fraenkel &
Wallen, 1996, p.237). After testing the hypothesis, it is found that there is a
statistically significant change in students’ spatial ability scores across three time
periods (pre-treatment, post treatment and retention) (p<0.05). In other words,
there are significant mean rank differences in the spatial ability sores across the
three time periods. The mean rank of PRESAT, POSTSAT and RETSAT scores
are 1.05, 3.00 and 1.95 respectively. To determine which mean ranks of the test
scores cause this difference, the Wilcoxon test is used. The results are given in
Table 4.4.
54
Table 4.4 Wilcoxon signed Rank Test results for SAT scores of students
Tests
POSTSAT PRESAT
RETSAT POSTSAT
RETSAT PRESAT
Type of
Ranks
Negative
Ranks
Positive
Ranks
Negative
Ranks
Positive
Ranks
Negative
Ranks
Positive
Ranks
n
Mean Rank
Sum of
Ranks
0
.00
.00
Sig.
0.00
21
11.00
231.00
21
11.00
231.00
0.00
0
.00
.00
1
1.00
1.00
0.00
20
11.50
230.00
The Table 4.4 shows that there is a significant difference between mean
ranks of the POSTSAT scores and the PRESAT scores (p < 0.05). The mean rank
of POSTSAT scores is statistically significantly greater than their mean rank of
PRESAT scores (Mean Rankpostsat= 3.00 and Mean Rankpresat =1.05). In addition,
the mean rank of RETSAT scores is statistically significantly less than their mean
rank of POSTSAT scores (Mean Rankretsat =1.95, Mean Rankpostsat= 3.00). Lastly,
the mean rank of RETSAT scores is statistically significantly greater than their
mean rank of PRESAT scores (Mean Rankretsat =1.95, Mean Rankpresat= 1.05).
The second sub-problem of the first main problem is: “Is there a statistically
significant change in students’ spatial orientation scores across three time periods
(pre-treatment, post treatment and retention)?”
For the second sub-problem the following hypotheses is stated:
H01.2 “There is no statistically significant change in students’ spatial
orientation scores across three time periods (pre-treatment, post treatment and
retention)?”
To test this hypothesis, one-way repeated measures ANOVA is used. One of
the main assumptions is the normality assumption. The normality assumption for
SOAT is determined by Kolmogorov-Smirnov statistics. Since the sig. values
55
were found .200 for PRESOAT scores, .200 for POSTSOAT scores and .200 for
RETSOAT scores the normality assumption is satisfied. (p > 0.05).
Table 4.5 Results of one-way repeated measures ANOVA for SAT scores
with respect to time
Effect
Value
F
Sig.
Partial Eta
Squared
Observed
Power
Wilks’ lambda
.169
46.739
.000
.831
1.000
To test hypothesis, one-way repeated measures ANOVA was performed.
After testing hypothesis it was found that there was a significant effect for time
(Wilk’s lambda= .000, F (2, 19) =46,739,
p= .005). The partial eta-squared is
found as 0.83. This result suggests very large effect size by utilizing guidelines
proposed by Cohen (1988). To find out which pairs of time periods caused the
mean difference scores of spatial ability, LSD comparisons were used. The results
were given in Table 4.6.
Table 4.6 Pairwise Comparisons of SOAT scores of students
(I)
time
1
2
3
(J) time
Mean
Difference
(I-J)
Std.
Error
Sig.
2
3
1
3
1
2
-43.381
-20.762
43.381
22.619
20.762
-22.619
4.710
3.940
4.710
2.779
3.940
2.779
.000
.000
.000
.000
.000
.000
95% Confidence
Interval for
Difference
Lower
Upper
Bound
Bound
-53.207
-33.555
-28.981
-12.543
33.555
53.207
16.823
28.415
12.543
28.981
-28.415
-16.823
All three means were significantly different from each other. Mean spatial
orientation score was significantly higher immediately after the visual treatment
(M = 89.95, SD=23.09) than before the treatment (M = 46.57, SD=13.01). The
mean performance score one month later was significantly lower (M = 67.33,
56
SD=18.14) than that immediately after the treatment, but significantly higher than
the mean performance before the treatment
It is by Friedman Test at the significance level 0.05. After testing the
hypothesis, it is found that there is a statistically significant change in students’
spatial orientation scores across three time periods (pre-treatment, post treatment
and retention) (p<0.05). In other words, there are significant mean rank
differences in the spatial orientation sores across the three time periods. The mean
rank of PRESOAT, POSTSOAT and RETSOAT scores are 1.00, 3.00 and 2.00
respectively. To determine which mean ranks of the test scores cause this
difference, the Wilcoxon test is used. The results are given in Table 4.7
Table 4.7 Wilcoxon signed Rank Test results for SOAT scores of students
Tests
POSTSAT –
PRESOAT
RETSAT POSTSOAT
RETSAT PRESOAT
Type of
Ranks
Negative
Ranks
Positive
Ranks
Negative
Ranks
Positive
Ranks
Negative
Ranks
Positive
Ranks
n
Mean Rank
Sum of
Ranks
0
.00
.00
Sig.
0.00
21
11.00
231.00
21
11.00
231.00
0
.00
.00
0
.00
.00
21
11.0
231.00
0.00
0.00
The Table 4.7 shows that there is a significant difference between mean
ranks of the POSTSOAT scores and the PRESOAT scores (p < 0.05). The mean
rank of POSTSOAT scores is statistically significantly greater than their mean
rank of PRESAT scores (Mean Rankpostsoat= 3.00 and Mean Rankpresoat =1.00). In
addition, the mean rank of RETSAT scores is statistically significantly less than
their mean rank of POSTSAT scores (Mean Rankretsoat =2.00, Mean Rankpostsoat=
3.00). Lastly, the mean rank of RETSOAT scores is statistically significantly
greater than their mean rank of PRESOAT scores (Mean Rankretsoat =2.00, Mean
Rankpresoat= 1.00).
57
The third sub-problem of the first main problem is: “Is there a statistically
significant change in students’ spatial visualization scores across three time
periods (pre-treatment, post treatment and retention)?”
For the third sub-problem the following hypotheses is stated:
H01.3 “There is no statistically significant change in students’ spatial
visualization scores across three time periods (pre-treatment, post treatment and
retention)?”
To test this hypothesis, one-way repeated measures ANOVA is used. One of
the main assumptions is the normality assumption. The normality assumption for
SVAT is determined by Kolmogorov-Smirnov statistics. Since the sig. valuees
were .200 for PRESVAT scores, .200 for POATSVAT scores and .076 for
RETSVAT scores the normality assumption is satisfied. (p > 0.05)
Table 4.8 Results of one-way repeated measures ANOVA for SAT scores with
respect to time
Effect
Value
F
Sig.
Partial Eta
Squared
Observed
Power
Wilks’ lambda
.242
29.778
.000
.758
1.000
To test hypothesis, one-way repeated measures ANOVA was performed.
After testing hypothesis it was found that there was a significant effect for time
(Wilk’s lambda= .000, F (2, 19) =29,778,
p= .005). The partial eta-squared is
found as 0.76. This result suggests very large effect size by utilizing guidelines
proposed by Cohen (1988). To find out which pairs of time periods caused the
mean difference scores of spatial ability, LSD comparisons were used. The results
were given in Table 4.9
58
Table 4.9 Pairwise Comparisons of SAT scores of students
(I) time
1
2
3
(J) time
Mean
Differenc
e (I-J)
Std. Error
Sig.
2
3
1
3
1
2
-12.048
-6.810
12.048
5.238
6.810
5.238
1.567
1.417
1.567
1.002
1.417
1.002
.000
.000
.000
.000
.000
.000
95% Confidence
Interval for
Difference
Lower
Upper
Bound
Bound
-15.316
-8.779
-9.765
-3.854
8.779
15.316
3.148
7.329
3.854
9.765
-7.329
-3.148
All three means were significantly different from each other. Mean spatial
visualization score was significantly higher immediately after the visual treatment
(M = 29.10, SD=10.81) than before the treatment (M=17.05, SD=6.71). The mean
performance score one month later was significantly lower (M = 23.86,
SD=10.38) than that immediately after the treatment, but significantly higher than
the mean performance before the treatment.
It is by Friedman Test at the significance level 0.05. After testing the
hypothesis, it is found that there is a statistically significant change in students’
spatial visualization scores across three time periods (pre-treatment, post
treatment and retention) (p<0.05). In other words, there are significant mean rank
differences in the spatial visualization sores across the three time periods. The
mean rank of PRESVAT, POSTSVAT and RETSVAT scores are 1.12, 2.88 and
2.00 respectively. To determine which mean ranks of the test scores cause this
difference, the Wilcoxon test is used. The results are given in Table 4.10
59
Table 4.10 Wilcoxon signed Rank Test results for SAT scores of student
Tests
POSTSAT –
PRESOAT
RETSAT POSTSVAT
RETSAT PRESOAT
Type of
Ranks
Negative
Ranks
Positive
Ranks
Negative
Ranks
Positive
Ranks
Ties
Negative
Ranks
Positive
Ranks
Ties
n
Mean Rank
Sum of
Ranks
0
.00
.00
Sig.
0.00
21
11.00
231.00
18
11.28
203.00
2
3.50
7.00
2
3.75
7.50
18
11.25
202.50
0.00
1
0.00
1
The Table 4.10, shows that there is a significant difference between mean
ranks of the POSTSAT scores and the PRESVAT scores (p < 0.05). The mean
rank of POSTSVAT scores is statistically significantly greater than their mean
rank of PRESVAT scores (Mean Rankpostsvat= 2.88 and Mean Rankpresvat =1.12). In
addition, the mean rank of RETSVAT scores is statistically significantly less than
their mean rank of POSTSVAT scores (Mean Rankretsvat =2.00, Mean Rankpostsvat=
2.88). Lastly, the mean rank of RETSVAT scores is statistically significantly
greater than their mean rank of PRESVAT scores (Mean Rankretsvat =2.00, Mean
Rankpresvat= 1.12).
4.3. The results of the second main problem
4.3.1. The results of the interview related to thinking process in the
visual treatment
Researcher analyzed each interview by using phenomenographic method to
summarize findings about each question. A phenomenographic analysis seeks a
"description, analysis, and understanding of experiences" (Marton, 1981, p. 180).
Students’ speech was categorized with respect to their meaning and then students’
excerpted answers were fit in these categories. Tables for each question include
60
students’ opinion about visual treatment in terms of cognitive process and
feelings. Each table was designed to have one column for each cognitive process
and feelings category.
Table 1 demonstrated that the categories for the question “which solution
methods did you use for solving questions for the first time?” The purpose of this
question was to investigate the methods that students used before taking spatial
ability activities.
Table 4.11 The Results of First Interview Question
Answer Categories
Students’ Explanations
I tried to imagine in my mind (st1)
I tried to construct shapes in my mind (st2)
For example, I tried to imagine the cubes in my
mind in the cube comparison questions. I
usually tried to find the symmetry of the shapes
Imagining.
in my mind. I tried such kind of methods in the
(Sts.1,2.3.4.6.7,8.9)
card rotation questions. (st3)
I tried to imagine the shapes in my mind. I
dreamed and solved questions by using this
method. (st4)
I tried different solving methods, while solving
the questions. I tried to solve questions by
Imagination in the mind. I tried to find the
shapes on unseen faces. I imagined shapes in
my mind. (st6)
61
Table 4.11 (continued)
Answer Categories
Students’ Explanations
I say that "if I turn the shapes in my mind, it
would turn into such condition.” I solved it by
means of using this way. (st7)
I made an effort to find the answer by
imagining the shapes, while solving the
questions. (st8)
I made an effort to solve the questions by
imagination. I sometimes rotated the question
paper. (st9)
Seeking a pattern. (st1)
I made an effort to seek a pattern for solving
questions. (st1)
Looking at sample solutions.
I examined the sample solutions and tried to
(Sts.2,5)
understand
the
logic
while
solving
the
questions. (st2)
While solving the questions, I examined the
sample solutions. I made an effort to find a
suitable method for me. (st5)
Estimating. (st.7)
I tried to solve questions by imagination. I said
if I turned the shape, it would be something like
that and solved them by using this method (st7)
As it is seen in the table, students’ solving methods were categorized into 4
subgroups which were; imagining, seeking a pattern, looking at sample solution,
and estimating. When the students’ answers were analyzed, a similar tendency
was observed to select imagining method. Related to the interview question,
62
almost all students stated that they tried to imagine the geometric shapes in their
mind and tried to solve questions by selecting appropriate transformation
movements. For example st6 used mental picture to found drawings on unseen
faces in card rotation question and expressed his thoughts as:
“I tried different solving methods, while solving the
questions. I tried to solve questions by imagination in the
mind. I tried to find the shapes on unseen faces.”
Moreover, st.1 stated that he used combination of seeking a pattern and
imagining together.
Sts. 2 and 5 attempted looking at sample solution to conclude the right
answers. In my opinion which was gained from the interview with these students,
they just only used sample question solving method to got an idea about which
solving method could be used but they had same trouble with express their
thinking
As it understood from the table estimating was not the only method used by
st7. He used the combination of estimating and imagining of the shapes in mind.
In general imagine the geometric shapes in mind was used by nine students
expect st5. Seeking a pattern was used by one student, examine the sample
question solving was used by two students and estimating method was used by
only one student.
Table 4.12, displayed that the categories for the question “Did your solving
methods show changes respect to question types in spatial ability tests?” The
purpose of this question was to investigate whether students’ problem solving
method show changes within test types
63
Table 4.12 the Results of Second Interview Question
Answer Categories
Didn’t
show
(Sts.1,2,4,5,6,7,8,9)
change
Students’ Explanations
I used the same methods for the tests. I didn’t use
different methods. I made an effort to imagine in
my mind.(st1)
No, my solving methods didn't show any
difference. I solved all of these questions by using
these methods. These methods are imagining and
rotating shapes in the mind (st2)
I generally used the same methods. I tried to
solve all of the questions by imagining in my
mind. (st4)
Generally, I used same methods. I tried to solve
the questions by looking at sample questions
while solving the first tests. (st5)
I used the same methods while solving the
questions again. I tried to solve them by
imagining. (st6)
No, it didn't show any change. I tried to solve the
tests by imagining. (st7)
That’s to say, I answered all the questions using
the same method. I didn't use any other methods.
(st8)
No, I always used the same method. My method
didn’t show any change with respect to the
question types. (st9)
64
Table 4.12 (continued)
Answer Categories
Students’ Explanations
Show changes (st3)
Sometimes I did. For example, I
solved he card rotation questions by
using symmetry and rotating in the
mind methods. (st3)
As it is seen in the table, students’ solving methods were categorized into 2
subgroups which were: didn’t show changes and show changes
Almost all students expect st3 explained that he/she did not use another
method different than he/she used in the first test. St2 who used imagination as a
problem solving method expressed his thoughts as;
“No, my solving methods didn't show any difference. I
solved all of these questions by using these methods. These
methods are imagining and rotating shapes in the mind.”
Different than the other student, st3 expressed that he/she used finding
symmetry and imagine in mind together for solving questions and expressed his
thoughts as;
“Sometimes I did. For example, I solved he card rotation
questions by using symmetry and rotating in the mind
methods.”
It is definitely understood from the students’ responses that problem
solving methods did not show changes within spatial ability tests. In other words,
problem solving methods given in the table 4.11 were used in all; cube
comparison, card rotation, surface development and paper folding tests without
feel necessity of any other solving method.
65
Table 4.13 showed the categories for the question “Did your solving
methods show changes after activities? For example, how had you solved
questions before the activities, how did you solve questions after the activities?
What kind of solving method did you develop for solving cube comparison
questions?” The purpose of this question was to got investigate the changes in
methods and effects of activities on it
Table 4.13 The Results of Third Interview Questions
Answer Categories
Students’ Explanations
Seeking a pattern
When I made the cube comparison questions, I tried to
(Sts.1,7)
seek a pattern on the shapes. I tried to understand which
shapes would come after which shape.(st1)
I was solving questions by imagination before the
activities but I tried to rotate I tried to perform cube
comparison questions by imagining while solving the
first tests. Afterwards, I tried to solve the again by
seeking a pattern.(st7)
I made an effort to solve the cube comparison questions
by imagining them in my mind.(st2)
Imagination in the
mind (Sts. 2,8,9)
I used the imagination method. I tried to guess which
shape to come after the shape on the surface of the
cube. If the shapes match one another, this means that
cubes were the same if not they weren’t. Imagination
was clearer after doing the activities. (st8)
In the beginning, I didn’t know how to handle
questions. However after the activities, I tried to answer
the questions by imagining. I tried to find which shapes
would come after which movement. (st9)
66
Table 4.13 (continued)
Answer Categories
Students’ Explanations
Perception of
Perceiving the front and back faces of the cubes become
surface (st3)
easier after doing the activities. I solved those questions
faster. At the first activity, I had got more undone
questions, but after the activities the number of undone
questions gradually reduced. (st3)
Turning in the
shapes in my mind and I gave attention to shapes which
mind (Sts. 4,6)
come to the front surfaces after the activities. (st4)
I firstly thought how I could found the shapes that were
on unseen surfaces of the cubes. I rotated shapes in my
mind for finding these shapes. (st6)
Giving numbers to
While I was solving the questions again, I gave numbers
surface of the
for the shapes on the cubes. I compared the shapes with
shapes (st5)
numbers. I understood that I could remember the numbers
more easily than remembering the shapes. (st5)
As it is seen in the
table, students’ problem solving methods were
categorized into 5 subgroups which were; seeking a pattern, imagination in the
mind, perception of surface, turning in the mind, and giving number to surface of
the shapes.
Sts.1 and 7 stated that they used seeking a pattern as a problem solving
method in the second application of cube comparison test. St1 explained that his
problem solving method did not show change with respect to first application.
However, method used in the second application was more successful than the
first one. He tried to find shapes alternately on the cubes. Although, the st7 used
guessing as a solving method in the first cube comparison test, he used seeking a
67
pattern in the second application.
According to information had from sts. 2, 8 and 9 it was understood that
their problem solving method did not show changes in respect of first and second
cube comparison test application. They used imagination in mind as a problem
solving method. St8 manifested that appearing image in the mind was clearer and
moving it was easier in the second application with respect to first one.
St3 denoted that it was easy to perceive the faces of cubes in the second
application and expressed his thoughts as;
“Perceiving the front and back faces of the cubes become
easier after doing the activities. I solved those questions
faster. At the first activity, I had got more undone
questions, but after the activities the number of undone
questions gradually reduced.”
Sts. 4 and 6 explained that they used rotation in the mind as a problem
solving method. Their problem solving method showed a change with a small
difference.
St5 defined that he gave numbers to the cube faces and match them with
shapes. The reason giving numbers to the face of the shapes was being easy to
remember numbers than remembering shapes.
Table 4.14 showed the categories for the question “Which solving method
did you use for solving card rotation questions after the activities?” The purpose
of this question was to investigate the changes in methods used in card rotation
questions and effects of activities on it.
68
Table 4.14 The Results of Fourth Interview Questions
Answer Categories
Students’ Explanations
Turning in the mind (Sts. 1,2,7,8,9) I tried to solve the card rotation questions
by turning the shapes in my mind.(st1)
I also tried to solve the card rotation
questions by turning the shapes in my
mind.(st2)
I tried to turn the shapes in my mind and
my
decision
was
based
on
this
movement.(st7)
In the beginning, I tried to solve these
questions again by turning the paper.
Afterwards, I tried to make a decision for
whether the shapes were the same or not
by turning shapes in my mind(st9)
Firstly, I looked at the first shape and then
asked shape. I tried to rotate the shapes in
the asked questions for making a decision
about whether the asked and given shapes
were the same. (st8)
Looking at the previous shape (Sts.
At the first activity I was solving the card
3,6)
rotation questions consistently by looking
at the initial shape, but after the activities
I made a decision by looking at the
previous
69
Table 4.14 (continued)
Answer Categories
Students’ Explanations
shapes. That is to say if the initial and the
first asked shapes were the same, and also,
the first asked and the second asked shapes
were the same, that meant the initial and
the second asked shapes were the same.
(st3)
While
answering
the
card
rotation
questions, I always made decisions by
considering the initial shape. But after the
activities I tried to make a decision by
looking at previous shapes. (st6)
By controlling symmetry (Sts 4,9) At first, I tried to rotate shapes in my mind
but then, I gave attention to whether the
shapes were symmetrical or not. I realized
that if the shapes were symmetrical they
were not the same. (st4)
I gave attention to whether the shapes were
symmetrical or not. I realized that two
symmetrical shapes cannot be the same.
(st9)
Giving the letter to the shapes
I named each corner of the shapes by a
(st5)
letter
for
solving
the
card
rotation
questions. After I turned the shapes, I tried
to find the new places of the letters. My
decision was based on this logic. (st5)
70
As it is seen in the table, students’ problem solving methods were
categorized into 4 subgroups which were Turning in the mind, Looking at the
previous shape, By controlling symmetry, Giving the letter to the shapes;. When
the answers of students were analyzed, it was seen that students’ problem solving
method showed changes and their thinking style got more deeply into spatial
ability problems when comparing with first application.
Sts. 1, 2, 7 and 9 stated that rotation in the mind was used as a solving
method for card rotation questions.
Sts. 3 and 6 denoted that they tried to solve questions by looking at previous
shape and getting it as a reference. They determined whether the asked shape
same, by rotating leading shape in the first application. However, their solving
method had showed changes after the activities. They started took up previous
shape as a reference instead of leading shape and st6 explained the method as
follows;
“While answering the card rotation questions, I always
made decisions by considering the initial shape. But after
the activities I tried to make a decision by looking at
previous shapes.”
Controlling symmetries was the method used by sts.4 and 9. Their solving
method was based on determining whether the asked shape was symmetrical with
leading shape or not. If the shape was symmetrical with leading shape they
understood that shapes were not the same if not vice versa.
Giving letters to the corners of the shapes was another method used by st5.
He/she stated that decision was depending on the position of letters on the shape.
If the letters brought into correct line after the rotation, this means that shapes
were same if not vice versa.
St8 stated that he looked at the leading shape, and then tried to rotate
leading shape to obtain the asked shape. If he obtained the asked shape by rotating
leading shape this means that shapes were the same, if not they weren’t.
71
Table 4.15 showed that the categories for the question “’which problem
solving methods did you used for paper folding?” The purpose of this question
was to got investigate the changes in methods used in paper folding questions and
effects of activities on it
Table 4.15 The Results of Fifth Interview Questions
Answer categories
Folding in the mind
(Sts.1,3,4,7,8,9)
Students’ Explanations
I tried to solve questions by folding paper in
my mind. I tried to find where the hole was.
(st1)
In the beginning, I wasn’t able to solve the
paper folding questions but after the activities
I could fold and open papers in my mind.
(st3)
While folding the paper, I tried to understand
where the hole could be.
I tried to
understand the place of hole by folding and
opening shapes in my mind. (st4)
While solving the paper folding questions, I
tried to find the place of hole in my mind. I
was eliminating irrelevant choices and I was
pointing the most logical one(st7)
I tried to find the answers of paper folding
questions by folding and opening shapes in
my mind(st8)
72
Table 4.15 (continued)
Answer categories
Students’ Explanations
Before the activities, I tried to find the place
and number of the holes by eliminating
choices. After the activities, I could find the
number and place of the holes in questions
with less folding but I still had trouble about
questions with more folding. I tried to find
the place of holes by opening shapes in my
mind. (st9)
Estimating (Sts. 2,5)
While solving the paper folding questions, I
tried to estimate where the holes could be.
(st2)
That is to say, I paid the attention to place the
folding lines of the paper. I tried to estimate
the place of the hole with respect to this
place. For example, If the folding line was
near the middle, the holes had to be near. If
those lines were near the corner, the holes
had to be distant. (st5)
Imagination (st6)
For the first time, I had trouble in the paper
folding questions. Afterwards, I started to
enjoy them. While I was solving the
questions again, I used the imagining
method. I tried to find where be holes could
be by imagining. (st6)
73
As it is seen in the table, students’ problem solving methods were
categorized into 3 subgroups which were; folding in the mind, estimating and
imagination
Almost all students expect sts. 2, 5 and 6 explained that folding in the mind
was the problem solving method that they used in the second paper folding test
application. Moreover st7 student used elimination of irrelevant choices and
folding in the mind as a problem together. Although elimination of irrelevant
choices had been used in the first application of test, folding in the mind was
selected as a problem solving method in the second application by st9. However
he thought that questions with high number of folding was still very difficult for
him to fold and open in mind
Sts. 2 and 5 expressed that guessing was the problem solving method used
in second paper folding application. They used guessing for finding correct places
of dots. If folding paper was pierced from place near center, dots formed closely,
if pierced place near to corners dots formed apart from each other.
St6 stated that paper folding questions were the most difficult questions that
he dealt in the first application expressed his thoughts as follows:
“For the first time, I had trouble in the paper folding
questions. Afterwards, I started to enjoy them. While I was
solving the questions again, I used the imagining method. I
tried to find where be holes could be by imagining.”
Table 4.16 demonstrated that the categories for the question “’what kind of
method did you follow for finding number of hole on folding papers?” The
purpose of this question was to investigate the strategy that students used.
74
Table 4.16 The Results of Sixth Interview Questions
Answer Categories
Students’ Explanations
Giving attention to number of folding In order to find the number of holes, I
(Sts. 1,2,3,4,5,6,7,8)
tried to pay attention to how many
sheets I folded. That is to say, the
numbers of the holes and folding
sheets were increasing together. For
example, when we folded the paper
twice two holes appeared. When we
fold
twice
again
four
holes
appeared(st1)
I tried to find the number of the holes,
by thinking of the number of folding
sheets. (st2)
In order to find the number of holes, I
counted the folding sheets. If I folded
the paper twice, two holes appeared; if
I folded again four holes appeared.
(st3)
I paid attention to the number of
folding sheets, when I tried to find the
number of holes. That is to say, when
we folded the paper twice, two holes
appeared. (st4)
I paid attention to the places where the
paper was folded. (st5)
75
Table 4.16 (continued)
Answer Categories
Students’ Explanations
For example, while I was solving such
questions for the first time, I supposed
that there would be one hole on the
paper. After the activities, I realized
that after one folding two holes
appeared on the paper. (st6)
I had difficulty in finding the number
of holes in the beginning, but then I
realized that the number of holes was
increasing together with the number of
folding. (st7)
It was very difficult for me to find the
number
of
the
holes.
Then,
I
understood that the number of the
holes was increasing along with the
number of the folding. (st8)
Folding shapes in the mind (st9)
I tried to imagine the shapes of the
folded paper in my mind and also to
open those shapes in my mind. I
counted the number of holes during
this opening process. (st9)
As it is seen in the table, students’ problem solving methods were
categorized into 2 subgroups which were; giving attention to folding number of
folding and Folding shapes in the mind
76
Almost all students except st9 specified that they found the number of holes
on the paper by giving attention to number of folding. Students stated that there
was a directional proportion with the number of holes and folding number.
Students discovered that if the paper was folded once, two holes were appearing.
If the same paper was folded once again, the hole number got twice and this
logarithmic increase continued with the number of folding. Sts 7 and 8 discovered
that number of holes was increasing with the folding. However, finding the exact
number of hole was still a problem for them. St. 6 expressed his thoughts as
follows;
“For example, while I was solving such questions for the
first time, I supposed that there would be one hole on the
paper. After the activities, I realized that after one folding
two holes appeared on the paper.”
St9 explained that he counted the number of holes appearing on the paper by
opening folded shapes in the mind. This solving method was similar to the method
used by other students. However, st9 emphasized on the usage of imagining in the
mind method much more than the other students.
Table 4.17 showed the categories for the question “Which lectures were
related with activities? Could you please explain it with examples?” The purpose
of this question was to understand whether or not students put connection between
spatial ability activities and lectures.
Table 4.17 The Results of Seventh Interview Questions
Answer Categories
Mathematics (Sts.1,2,3,4,5,7,9)
Students’ Explanations
For example, the questions that, were
asked to solve perspective drawing of
shapes from different point of view in
mathematics lecture were similar to
the activities.(st1)
77
Table 4.17 (continued)
Answer Categories
Students’ Explanations
Activities and the geometry subjects
resembled to one another. For example
the subject, drawing perspective drawing
of geometric shapes.(st2)
The subject drawing the opened form of
different geometric shapes performed in
mathematics lecture resembled to the
activities. (st3)
I was unsuccessful at drawing opened
form of three dimensional geometric
shapes in mathematics lecture. However,
after the activities, I achieved to solve
these types of questions more easily. (st4)
In my opinion, the subject finding
symmetries of shapes in mathematics
lecture resembled to the activities. (st5)
I think that finding symmetries of
geometric shapes and drawing them were
related with activities. (st7)
Activities
helped
me
to
solve
the
questions that were asked to draw views
of cubes from different angles such as
front, top and behind. That is why I
believed that activities were mostly
related with mathematics. (st9)
78
Table 4.17 (continued)
Answer Categories
Technology and design (Sts.(6,8,9)
Students’ Explanations
Our technology and design lecture
teacher requested from us to construct
a structure by using the plastic glasses.
I constructed a shape without bases in
turning form .The most admired
project
was
mine.
This
project
resembled to the activities (st6)
Our technology and design lecture
teacher requested from us to construct
different
different
models
by
combining
geometric
shapes.
Pentominoes activity was related with
this construction. (st8)
Our mathematics teacher requested
from us to find a geometric shape
which has not invited yet. I tried to
find
different
shapes
by
using
knowledge gained from origami. (st9)
As it is seen in the table, students’ problem solving methods were
categorized into 2 subgroups which were; mathematics and technology-design
lectures
Most of the students stated that activities were related with mathematics.
For example, orthographic drawing was one of the activities that was related with
mathematics. The reason for giving this example by the students was the
similarity of activity and math subject. St9 expressed that orthographic drawings
79
were performed better than the days before activities. Because of that reason, he
thought that activities were related with mathematics.
Sts. 3 and 4 stated that finding the open frame of three-dimensional
geometric shapes in mathematics lecture was similar to activity we performed.
Because of that reason they believed that activities were related with mathematics.
Sts. 5 and 7 expressed that they found a relation between shading reflection
activity and finding the symmetry of a figure subject in mathematics lecture.
Thence the idea activities were relevant with mathematics appeared.
Sts. 6, 8 and 9 denoted that activities were mostly related with technology
and design lecture. St6 explained that gaining acquired from activities helped him
to construct a building design made up of plastic glasses without any attachment.
Number St8 believed that activities were related with technology and design
lecture because; pentaminoes facilitated him to constitute a picture by connecting
different geometric shapes in a manner. St9 tried to find an unknown geometric
shape as a technology-design lecture’ project by using techniques acquired from
origami activities and expressed himself as;
“Our mathematics teacher requested from us to find a
geometric shape which has not invited yet. I tried to find
different shapes by using knowledge that is gained from
origami.”
Table 4.18 showed that the categories for the question “ Do you think that
the time passing between second and third application period had positive or
negative effects on you in solving third application questions?” The purpose of
this question was to have opinion about students thinking process about the timebreak given to the students for four weeks after the post-treatment.
80
Table 4.18 The Results of Eight Interview Questions
Answer Categories
Students’ Explanations
Negative effect (Sts. 1,2,3,4,5,6,7,8,9)
In my opinion, this time interval
caused negative effect on me. It was
more difficult for me to solve third
application question when comparing
with second application. That's to say
we didn’t perform the activity hence I
forgot how to solve questions. (st1)
I found questions a bit difficult in third
application. I had difficulty in solving
questions. Probable reason was the
time interval experienced without any
activity. (st2)
Solving third application questions
was easier than first application. I
think that giving a break to the
activities caused to decrease my
spatial knowledge. Therefore, I think
that time without any activity affected
me in negative manner. (st3).
I believe that this time break caused a
negative affect on me. After I left to
perform activities, solving questions
got more difficult for me. (st4)
81
Table 4.18 (continued)
Answer Categories
Students’ Explanations
I found questions more difficult, after
we left to deal with activities. As we
didn’t perform activities, I forgot how
to solve questions. (st5)
It caused negative affect on me.
Solving thesis questions was more
difficult for me after we left to solve
activity questions. (st6)
I found questions a bit strange.
Because we didn't solve activity
questions for a long time, I forgot the
methods that I use for solve questions.
(st7)
This
experienced
time
without
performing activities caused to forget
knowledge gained from the activities.
(st8)
In my opinion, It caused negative
effect on me; After I left to perform the
activities, I had difficult in solving
third application questions(st9)
All students stated that time interval that experienced without any visual
treatment affected their spatial knowledge ability negatively. Almost all students
stated that they forgot how to handle spatial ability problems and had some
difficulty in solving questions. Sts. 1 and 3 stated that solving third application
82
questions were more difficult when comparing with second application. However,
st3 explained that solving third application questions were easier than first
application questions and expressed his/her thoughts as follows;
“Solving third application questions was easier than first
application but more difficult than second one. I think that
giving a break to the activities caused to decrease my
spatial knowledge. Therefore, I think that time without any
activity affected me in negative manner.”
This explanation showed that giving a break to visual treatment caused to
forget knowledge gained from activities but loss of knowledge was limited.
Otherwise, it couldn’t possible for students to get high score at third application
when comparing with first application. This result was consistent with inferential
findings of this study.
4.3.2. The results of the interview related to feelings toward the visual
treatment
Table 4.19 shows that the categories for the question “What did you feel
when you faced with spatial ability questions for the first time?” The purpose of
this question was to examine the effects of spatial ability questions on students’
feelings.
Table 4.19 The Results of Ninth Interview Questions
Answer Categories
Fear (st1)
Students’ Explanations
It was the first time that I faced such kind
of questions; I feared that I wouldn't be
able to solve the questions. I had never met
such types of questions before. (st1)
Being sad (st9)
I said I wouldn’t be able to solve questions
and I got sad. (st9)
83
Table 4.19 (continued)
Answer Categories
Being tensed (Sts.4,5,7)
Students’ Explanations
I get tensed because I thought that
given time to finish test wouldn't be
enough for me. (st4)
I get tensed since; I thought that I
wouldn't have solved the questions.
(st5)
Since, I had never faced such a thing, I
coerced insistently and I got tensed.
(st7)
Being worried (st6)
I found questions very worrying.
Because I didn’t know anything and I
hadn't any idea about how questions
would be solved. I got a bit worried
while I was solving the questions. (st6)
Being nervous (st8)
When I saw the questions, I thought
that what I would made and I got
nervous (st8)
Enjoyment (Sts.2,3)
I found questions very interesting.
Questions were similar to a game.
While I was solving the questions,
I had difficulty but it's true that I
enjoyed myself. (st2)
The questions very difficult and I had
never faced with such kind of questions
84
Table 4.19 (continued)
Answer Categories
Students’ Explanations
before. But it was enjoyable to try to
solve questions. (st3)
Being excited (Sts.4,5)
It was the first time that I faced with
such kind of questions and I got
excited (st4)
I
found
questions
different
and
stranger that is why I got excited (st5)
As it is seen in the table students’ feelings were categorized into 7
subgroups which were: Fear, being sad, being tensed, being worried, being
nervous, enjoyment and being excited. Most of the students’ feelings were
negative when they faced with spatial ability problems.
St1 said: “I was afraid of not being able to solve spatial ability questions
when I faced spatial ability questions for the first time”. Moreover he said it was
the first time that he dealt with this kind of question types.
Sts. 2 and 3 denoted that they entertained during this forty-minute time that
dealing with spatial ability questions. Both of these two students find questions
difficult and entertaining.
Students with number 4, 5 and 7 expressed themselves get tensed. Because
they thought not being able to solve questions. In addition to this, sts. 4 and 5
were excited different than st7. The reason for those feelings was being the first
time that they faced with such kind of questions.
St8 felt affection because, he thought not being able to solve questions when
he faced with the questions. St6 was worried about solving method of questions,
85
with the same reason of st8. The reason was not being able to solve the problems
and expressed him as:
“I found questions very worrying. Because I didn’t know
anything and I hadn't any idea about how questions would
be solved. I got a bit worried while I was solving the
questions.”
While 5 categories included negative feelings, 2 of them included positive
feelings. Four of the students felt negative and positive feelings together when
they firstly faced with spatial ability problems.
Table 4.20 presented that the categories for the question “What did you feel when
you realize that your solving method failure at the first time?” The purpose of this
question was to investigate students’ feelings when they had trouble about their
problem solving method
Table 4.20 The Results of Tenth Interview Questions
Answer Categories
Fear (st1)
Students’ Explanations
The thinking not being able to solve questions
caused to get fear and I left these questions undone
(st1)
Being demoralized (Sts. I found questions a bit difficult and felt myself
2,3,4,5)
demoralized. I couldn’t able to think what I would
make and I left answer undone in such questions.
(st2)
I thought that I wouldn't able to solve the questions,
so I become low. However, I said myself that I can
solve these questions and I tried to apply different
solving methods to the questions. (st3)
86
Table 4.20 (continued)
Answer Categories
Students’ Explanations
I felt myself demoralized when my solving method
was failure. (st4)
When I didn’t solve the questions, I became low.
Although, I found questions very easy at the first
page, it became increasingly difficult in the
following pages. I thought that I wouldn't able to
solve those difficult questions at the last part. (st5)
Disappointment. (st6)
I was disappointed. (st6)
Being nervous (st7)
When I didn’t solve the questions I thought that I
wouldn't able to solve other questions. In addition to
this, given time to solve questions was limited so; I
did not finish solving questions. Therefore I felt
nervous. (st7)
Being panic (st8)
That’s to say, I felt in panic by thinking that I
wouldn't able to solve those questions. (st8)
Being angry (st9)
I got angry. I said that myself” I wouldn’t solve
those questions in no way.” I felt angry. (st9)
As it is seen in the table, students’ feelings were categorized into 6
subgroups which were; fair, being demoralized, disappointment, being nervous,
being panic and Being angry. All students’ feelings were negative when their
problem solving method of no avail. Students were expected to try other solving
methods at that time. However, students selected to leave questions empty.
St1 felt fear when his solving method was up to no good. He left question
87
blank instead of tried different solving method. Sts. 2, 3, 4 and 5 emphasized that
they got bored and depressed when their problem solving method failure. St2 said
that:
“I found questions a bit difficult and felt myself
demoralized. I couldn’t able to think what I would make
and I left answer undone in such questions.”
Moreover st5 signified that questions on 2nd pages of spatial ability problem
test were much more difficult than the questions on 1st pages. He got bored and
depressed especially in these pages.
St6 said that he frustrated when his solving method was of no avail
St7 expressed that he felt affliction while he realized that his solving method
was useless. Moreover, he thought that he would not be able to solve any other
questions from that point. Another reason for experiencing affliction was the
limited time given students to complete spatial ability test. He denoted his
conceptions as:
“When I didn’t solve the questions I thought that I
wouldn't able to solve other questions. In addition to this,
given time to solve questions was limited so; I did not
finish solving questions. Therefore I felt nervous.”
While the st8 expressed that he felt bad and live panic on account of
thinking about the test couldn’t be finished on time, st9 stated that he couldn’t
solve spatial ability question and this bring on feel unstrung
Table 4.21 presented that the categories for the question “What do you think
about activities we performed during 10-week? Did you enjoy or get bored what
do you feel in general?” The purpose of this question was to investigate students’
feelings during activities.
88
Table 4.21 The Results of Eleventh Interview Questions
Answer Categories
Students’ Explanations
Enjoyment (Sts 1,2,3,4,6,9)
I got enjoyed in the activities that we
construct square and rectangle by
using geometric shapes as well as
construct geometric shapes by using
cubes. (st1)
I enjoyed during the computer-based
activity, but the others were very
difficult. (st2)
Well, those activities were generally
very funny. I had a good time, when I
made an
effort
to
perform
the
activities. (st3)
I found activates very different and
enjoyable. I had never performed such
kind
of
activities
.So,
when
I
performed it, I had a good time. (st4)
I found the activities very enjoyable.
Especially, Tetris and origami which
required
combining
and
folding
shapes were very funny. (St6)
After
I
methods,
understood
I
activities. (st9)
89
enjoyed
the
solving
performing
Table 4.21 (continued)
Answer Categories
Students’ Explanations
Boring (Sts.2,5,6,7,8,9)
I found activities very boring. I didn’t
want to solve the questions. (st2)
However; I was in difficult in solving
questions that requires perspective
drawings. Those activities were very
boring. (st5)
I was impatient about performing
activities but I got bored during
difficult activities. (st6)
That’s to say the questions very
difficult, so I found activities very
boring. (st7)
Namely, the activities were a bit
boring. I strike, while I was making
the activities. So I can’t say that those
activities were enjoyable. (st8)
I got very bored when I couldn't solve
the questions. (st9)
As it is seen in the table, students’ feelings about activities were categorized
into 2 subgroups which were; enjoyment and boring
Almost all students found activities very entertaining. Two of the students
expressed that activities performed with manipulative such as construct cube and
pentominoes. They were the most enjoyable ones. St4 stated that it was the first
90
time that he engaged with such kind of activities, that is why he found activities
enjoyable. Although st6 found easy activities enjoyable, he got bored during hard
ones and emphasized his thoughts as:
“I found the activities very enjoyable. Especially, Tetris
and origami which required combining and folding shapes
were very funny. I was impatient about performing
activities but I got bored during difficult activities.”
St9 explained that activities were a bit boring during first two weeks. He
started to find activities more enjoyable with the adoption to activities and
understood how to perform them. He expressed himself as:
“I got very bored when I couldn't solve the questions.
After I understood the solving methods, I enjoyed
performing activities.”
Sts. 2, 7 and 8 affirmed that spatial ability activities were boring. St1
remarked that activities were very boring and difficult except computer based one.
According to my observation st1 get bored very early and tried to find excuses for
being absent during activity times. St7 stated that the reason for finding the
activities boring was difficulty of questions and had trouble to complete them. St8
said that:
“Namely, the activities were a bit boring. While I was
making the activities, I strike. So that I can’t say that those
activities were enjoyable.”
Table 4.22 presented that the categories for the question “Do you think that
activities helped you in solving thesis questions? I mean the questions you got
after 10-week period” The purpose of this question was to got vision of students
about what do they think about activities, did they put connection with activities
and asked questions
91
Table 4.22 The Results of Twelfth Interview Questions
Answer Categories
Usefulness (Sts.1.3.4.5.6.9)
Students’ Explanations
Yes, I think that those activities were
very useful. Questions and activities
were similar, so solving those questions
was very easy for me after the
activities.(st1)
Yes, activities assist me. Because some
of the questions were similar to those
questions we dealt in the activities.
Therefore, it assisted me. (st3)
Yes, I think that activities assisted me.
Performing activities provided me a
chance to make a practice. (st4)
Yes,
I
think
that
activities
were
beneficial for me. I was able to solve the
questions faster after the activities. (st5)
Yes, activities assisted me. I found
questions easier, and I solved the
questions faster after the activities. (st6).
Yes,
I
think
that
activities
were
beneficial for me. While performing the
activities, we were dealing with similar
questions. Therefore, solving questions
was easy for me. (st9)
92
Table 4.22 (continued)
Answer Categories
Students’ Explanations
Limited benefit (Sts.2,7)
Benefits of the activities were limited.
Because, activities and questions were
not similar to each other. (st2)
Yes, activities were a bit beneficial
for us solving questions was easier for
me after the activities. I accustomed to
solve such questions. (st7)
Being not beneficial (st8)
Those activities weren't beneficial for
me. I wasn't able to understand the
activities. I had trouble, while I was
solving the questions. (st8)
As it is seen in the table, students’ feelings about activities were categorized
into 3 subgroups which were; usefulness, limited benefit, being not beneficial
Based on this interview question, I began to look across all students’
responses in which activities affected students’ understanding to the spatial ability
questions and problem solving methods. Analysis of students’ responses helped
me to see how activities affected students’ point of view to the questions. It was
also understood from the table 4.22 that there was a general inclination to the
consideration that activities were beneficial in respect of solving spatial ability test
questions
Almost all students except Sts. 2, 7 and 8 specified that activities that were
performed for ten weeks assisted to solve spatial ability test questions. Related to
helpfulness of the activities, sts 1, 3 and 9 emphasized the similarity of activities
and spatial ability test questions. Students believed that this similarity let them to
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solve spatial ability test questions more easily. St4 stated that spatial ability
activities provided him a chance to practice and defined his thoughts as;
“Yes, I think that activities assisted me. Performing
activities provided me a chance to make a practice.”
Sts. 2 and 7 remarked that contribution of activities were limited. St2 stated
that activities were different than spatial ability question that is why contribution
was limited.
St8 student imported that activities did not provide help to solve spatial
ability questions and he expressed his thoughts as;
“Those activities weren't beneficial for me. I wasn't able to
understand the activities. I had trouble, while I was solving
the questions.”
Table 4.23 presented that the categories for the question “What did you
gained from the activities?” The purpose of this question was to got vision of
students about what kind of achievements did they gain after 10-activity-week.
Table 4.23 The Results of Thirteenth Interview Questions
Answer Categories
Students’ Explanations
Thinking style and ability (Sts.1,6)
I believe that, those activities have
improved my intellectual ability.(st1)
Activities provided me a different
thinking style especially in technology
and design lecture. (st6)
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Table 4.23 (continued)
Answer Categories
Creativity (st3)
Students’ Explanations
I think that, my creativity has improved.
I am able to have various thinking about
different circumstances. (st3)
Fast problem solving (Sts.3,5,7)
I am good at finding different solving
ways to the questions and solving the
questions faster after the activities. (st3)
Thanks to those activities, I was able to
solve spatial ability questions faster.
(st5)
Owing to the activities, I can solve the
questions faster (st7)
Looking situation from different
Those activities provided me a chance to
point of view (st4)
think better. I can look at the situations
from different point of view. (st4)
Solving
(Sts.4,5)
geometry
questions
I was successful in solving geometry
questions after the activities. I believe
that,
Iwill able to solve difficult geometry
questions anymore. (st4)
Owing
to
those
activities,
I
can
understand geometry concepts and solve
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Table 4.23 (continued)
Answer Categories
Students’ Explanations
questions of the three dimensional
shapes. (st5)
Drawing plan (st7)
I am getting more successful with
activities in drawing plan. (st7)
Imagining shapes in the mind (st9)
I was able to put shapes together and
imagine shapes in my mind. (st9)
Being not useful (Sts.2,8)
I don’t think that, those activities
provided me a lot of usefulness. (st2)
Like to my saying, I don’t think that
those activities provided a lot of
usefulness. (st8)
As it is seen in the table, students’ feelings about activities were categorized
into 7 subgroups which were; thinking ability-thinking style, creativity, fast
problem solving, looking situations from different point of view, solving
geometry questions, drawing plan , imagining shapes in the mind, being not
useful. Most of the students except sts2 and 8 believed that activities they
acquired different gaining by the help of activities.
While the students’ answers were examined, it was seen that almost each
students’ opinion about their achievements showed diversity.
Sts. 1 and 6
believed that activities caused to change his thinking style and ability. St3
predicated that activities enhanced his/her creativity. Moreover, st3 emphasized
that activities let her to solve questions more quickly than in normal times. sts.5
and 7 shared the same thought with st3 about solving questions more quickly
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According to st4, activities provided a chance not only to look at situations
from different point of view but also to being more successful in solving difficult
geometry questions. Moreover st5 thought that understanding and solving
geometry questions included three-dimensional geometric shapes were easier after
the activities. St9 stated that he could able to solve geometry questions with the
ability gained from the activities. He could put shapes together and imagine them
in his/her mind better.
St7 student, activities helped him to draw a diagram of a place and stated
him as;
“I am getting more successful with activities in drawing
plan.”
Sts. 2 and 8 thought that activities did not provide any gaining to them
Table 4.24 showed that the categories for the question “Why do you think
that these activities are so important? For example, do these activities were related
with daily life?” The purpose of this question was to get vision of students about
daily usage of spatial ability activities
Table 4.24 The Results of Fourteenth Interview Questions
Answer Categories
Drawing (Sts.1,6,7)
Students’ Explanations
I believe that, it is probable to come
on with application of activities in our
daily life. For example, I had trouble
about how to draw plan before the
activities. Nevertheless I can draw the
plan easily after the activities. (st1)
I believe that, activities are related
with our
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Table 4.24 (continued)
Answer Categories
Students’ Explanations
daily life. For example, my technology
and design teacher requested to construct
a house model. I firstly imagined inside
and outside of the house in my mind and
then drew the model of the house on a
paper. (st6)
I wasn't able to draw the plan of the
roads from our school to my home. After
those activities, I closed my eyes and
then imagined the roads, houses from
sky view in my mind and finally I drew
it easily. (st7)
Putting a mouse to a computer
Activities are related with our daily life.
case (st3)
For example, when I put the mouse
input, to the computer port, I found its
place easier.(st3)
Decoration of home (st4)
I believe that, activities are related with
our daily life. For example, we can use
our spatial ability to decorate our
furniture in our mind before put it into
practice.
Activities
enhanced
my
decoration ability. (st4)
Three dimensional thinking (Sts.5, I like drawing car models. I could only
9)
two-dimensional drawings of the car in
previous days, but now I can draw three
dimensional appearance of the car. (st5)
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Table 4.24 (continued)
Answer Categories
Students’ Explanations
I believed that activities are necessary
for solving geometry question that
required three-dimensional thinking
ability. (st9)
Limited usefulness (Sts.2,8)
I don’t think that activities provided
me a something (st2)
As I said before it was not beneficial
for me. (st8)
As it is seen in the table, students’ thoughts about daily life usage of spatial
ability activities were categorized into 7 subgroups which were; drawing, putting
the mouse to a computer case, decoration of home, three dimensional thinking,
limited usefulness
According to information got from sts. 1 and 7 it was difficult to drawing a
plan before spatial ability activities. However, after the activities drawing a plan
from a house to the school was performed better than the days before activities. In
addition to this st6 stated that he achieved to imagine house model before started
to construct it and to draw imagined model to a paper. St6 expressed his/her
thoughts as follows;
“I believe that, activities are related with our daily life.
For example, my technology and design teacher requested
to construct a house model. I firstly imagined inside and
outside of the house in my mind and then drew the model
of the house on a paper finally construct the house model
in respect of my drawings.”
St3 specified that putting the mouse input to the computer port was easy for
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her by just only looking at the mouse input, without looking at the computer port.
St4 declared that it was easy for her to arrange the furniture of their house in her
mind before put it into practice. St5 explained that he was capable of drawing two
dimensional car designs before spatial ability activities. However, he was up to
design three dimensional car pictures from different point of view after the
activities.
Sts 2 and 8 thought that there was no relation between spatial ability
activities and daily life. This result was consistent with findings from thirteenth
interview question. In that question students were asked to what you gained from
activities.
Table 4.25 showed that the categories for the question “’in which ability you
felt change after spatial ability activities?” The purpose of this question was to
investigate change occurred in students’ abilities after spatial ability activities.
Table 4.25 The Results of Fifteenth Interview Questions
Answer Categories
Solving
(Sts.1,7)
Students’ Explanations
the questions with shapes I didn't
want
to
solve difficult
questions and questions with shapes
formerly. But now, I can solve those
questions. That is to say, I am able to
find
the
different
solving
methods.(st1)
I can combine and imagine the
geometric shapes for solving questions
with shapes anymore. (st7)
Imagination of shapes in the mind I can imagine and open the geometric
(st2)
shapes in my mind. (st2)
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Table 4.25 (continued)
Answer Categories
Creativity (st3)
Students’ Explanations
My creativity has been improved. I
realized
that
I
have
different
intellectual abilities after the activities.
(st3)
Three dimensional thinking ability I think that, my three dimensional
(st4)
thinking ability has been improved
after the activities. (st4)
Drawing
three dimensional objects I think that my three dimensional
(st5)
drawing ability has been improved.
That’s to say I could draw only one
side of the car formerly. However, I
can draw the different sides of a car
anymore. (st5)
Solving questions faster (Sts. 6,9)
I could solve difficult questions faster
than the days before activities. (st6)
For example, I am able to solve
questions that were asked to find
perspective drawings of a construction
faster than the days before activities.
(st9)
No any change (Sts 2,8)
I don't think that the activities
improved my any ability. (st2)
I don’t think that activities helped to
enhance my abilities.(st8)
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As it is seen in the
table, students’ problem solving methods were
categorized into 8 subgroups which were; Solving the questions with shapes,
imagination of shapes in the mind, creativity, three dimensional thinking ability,
drawing three dimensional objects, solving questions faster, no any change.
St1 expressed that it was difficult for him to solve difficult geometry
questions before activities. However, he stated that he could find different solving
methods for these questions after the activities. In addition to this he could scratch
assisted geometry drawings after the activities and defined him as;
“I didn't want to solve difficult questions and questions
with shapes formerly. But now, I can solve those questions.
That is to say, I am able to find the different solving
methods.”
St2 explained that activities provided him a chance to imagine 3
dimensional geometric shapes in the mind. Moreover st3 believed that his
creativity changed with activities and explained his idea with examples here is the
conversation we had:
T: In which competence you felt change after the
activities?
St3: As I said before my creativity has improved after the
activities.
T: Could you please give me an example?
St3: For example, our technology and design teacher
requested to find a shape that is not found before. I
achieved to find different shapes
T: How did you find different kinds of shapes?
St3: I found different kind of shapes by folding papers.
T: Which geometric shapes did you use?
St3: I started with square and then I tried to find different
shapes by folding square in different directions
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T: Did you remember the name of activity which resemble
your solution method
St3: Yes, it was origami
St.4 explained that, three-dimensional thinking ability was developed with
the spatial ability activities. St4 specified his thoughts with examples. Here is the
conversation we had:
T: In which competence you felt change after the
activities?
St4: My three dimensional thinking ability has enhanced
after the activities
T: Could you please give me an example?
St4: I had some troubles about constructing three
dimensional geometric shapes and drawing the open form
of geometric shapes but I solved these kinds of questions
easily after the activities.
T: Which geometric shapes for example?
St4: For example, pyramids, prisms and the shapes you
were asked to us.
St.5 believed that his three dimensional drawing ability was developed with
activities. He explained that although he was capable of drawing car models from
one view, he could draw same car models from different point of views which
were front side and back
St9 expressed that understanding geometry questions, getting geometry
shapes together and imagining geometry shapes were easier than the days before
activities.
St6 thought that his time management ability for solving question was
developed with activities. He said that solving cube drawing from different point
of view in geometry lectures were faster than the days before activities
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Sts 7.8 believed that activities did not lead to any change in their abilities
4.4. Conclusions of the study
In the light of the above findings obtained by examining of each hypothesis,
the following conclusions can be deduced:
1. There is a statistically significant change in students’ spatial ability scores
across three time periods (pre-treatment, post treatment and retention)
2. There is a statistically significant change in students’ spatial orientation
scores across three time periods (pre-treatment, post treatment and retention)
3. There is a statistically significant change in students’ spatial visualization
scores across three time periods.
As a qualitative finding it was observed that visual treatment has positive
effects on students’ cognitive process in terms of their three-dimensional thinking
ability, creativity, solving spatial ability problems, imagination in the mind and
application of spatial ability in daily life. Moreover, visual treatment has positive
effects on students’ feelings in terms of develop positive attitudes toward both
lectures and spatial ability problems.
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CHAPTER 5
DISCUSSION AND RECOMMENDATIONS
This chapter includes discussion and interpretation of the results and some
recommendations for further studies. In the first section, restatement of some results
and discussion of these results are given. In the second section some
recommendations for further research studies are made.
5.1. Discussion of Findings
5.1.1. Discussion of Findings on Students’ Thinking Process
Many research studies were conducted in order to investigate the
relationship between spatial ability and other sciences such as mathematics,
geology, medicine, geology, engineering (Maier, 1996; Trindade, Fiolhais &
Almeida, 2002; Battista, Whealthy & Talsma, 1982; Wanzel, Hamstra, Caminiti,
Anastakis, Grober & Reznick, 2003; Olkun, Altun & Smith, 2005; Piburn,
Reynolds& McAuliffe, 2005). In addition to this, how to develop students’ spatial
ability by using different visual treatments was another important subject that was
investigated by the researchers (Clements & Owens, 1998; Alias, Black & Gray,
2003; Ben-Chaim, Lappan & Houang, 1985, 1988; Trindade, Fiolhais & Almeida,
2002; Waters, Gobet & Leyden, 2002; Ferk & Vratachic, 2003; Black, 2005;
Clements, Battista, Sarama & Swaminathan, 1997). However, students’ opinions
about visual treatment in terms of their feelings and cognitive process were not a
common issue handled by the researchers.
In this study, 6th grade elementary school students took nine different
activities within the context of visual treatment, which has performed by the
researcher for 10 weeks. The aim of the study was to investigate the development
of students’ spatial ability; spatial visualization and spatial orientation. In addition
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to this, nine randomly selected 6th grade elementary school students were
interviewed to have students’ opinions about the visual treatment in terms of
thinking process and feelings.
To test the effects of visual treatment on the students’ spatial abilities, oneway repeated measures ANOVA, Friedman and Wilcoxon tests were used. The
results showed that there was a statistically significant change in students’ spatial
ability, spatial visualization and spatial orientation scores across three time
periods (pre-treatment, post treatment and retention). Visual treatment activities
can be the main reason for this improvement.
It was quite important for researcher to have opinion about the methods
used by students to solve spatial ability problems before and after visual
treatment. Imagination was the most popular method used by the students before
visual treatment. The other methods were; seeking pattern, looking at sample
solutions and estimating. According to students’ explanations; these methods
didn’t change with respect to test types. However, methods that were used after
the visual treatment show specificity with respect to test types. For example while
students used seeking a pattern, perception of surface and giving numbers to
surface of shapes as a problem solving method in cube comparison test, they used
turning in the mind and controlling symmetry in card rotation questions.
Imagining in the mind was the most common method used by students both
before and after visual treatment. However, the number of questions which were
done and the number of correct answers were higher after visual treatment.
Conversation performed with st3 clarified this issue. He stated that activities
helped him to enhance his thinking ability and to imagine geometric shapes in his
mind. He explained the difference before and after activity as below;
T: You said you used imagining in the mind as a problem
solving method both before and after the activities.
However, the number of undone questions was less in
second application than in first application. What was the
difference?
St3. Imagination was more realistic in the second
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application. Shapes were appearing bad in the first
application
T: What do you mean by “appearing bad”?
St3: I couldn’t imagine the shapes properly.
T: Why do you think that imagination was better after the
activities?
St3: I got accustomed to such things after the activities.
These activities were very beneficial for me.
T: You mean, although you can’t explain how it happened,
your ability to imagine was better after the activities
Caroll (1993) defined spatial ability as mental skills concerned with
understanding, manipulating, reorganizing or interpreting relationships visually.
The two sub-skills of spatial ability which were spatial orientation and spatial
visualization were defined by Ekstrom et al. (1976). He defined spatial orientation
as an ability to visualize and mentally manipulate spatial configurations, to
maintain orientation with respect to spatial objects, and to perceive relationships
among objects in space and defined spatial visualization ability as the ability to
manipulate or transform the image of spatial patterns into other arrangements. The
findings of the study were discussed with respect to these definitions.
According to the results of the study, students’ spatial ability improved after
the visual treatment. One of the reasons for this improvement might be the
activities applied in the present study. For example, pentominoes activity that was
used for two weeks might be a reason. This activity was mostly related with
spatial orientation ability because it didn’t require manipulating spatial patterns
into other arrangements. According to my experience some of the students were
aware of the transformation geometry movements such as slide, flip and rotate
during the activities. Some also started to use the strategy to combine parts.
Moreover, some tried to join parts by rotating mentally.
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All students expressed in their interview that Pentominoes provided a help
to solve cube comparisons questions. This activity might affect the methods that
were used by students to solve cube comparison questions. Students used seeking
a pattern, imagination in the mind, perception of the surface, turning in the mind
and giving numbers to surface of the shapes as a problem solving method after
visual treatment. These methods were different than the methods before activities.
The main reason could be tendency to transfer the gaining and methods used in
the activities to the test problems. Because students stated there was a similarity
between activities and test problems. For example st1 used seeking a pattern
instead of imagination in the mind after the visual treatment. He expressed his
solving method as below;
“When I made the cube comparison questions, I tried to
seek a pattern on the shapes. I tried to understand which
shapes would come after which shape.”
Another student who changed his solving method after the activities was
st3. Although he used imagination in the mind before the activities, he used
perception of surface after the activities. He tried to determine whether the given
cubes were same, by perceiving the surface of cubes and solved problems faster.
St3 expressed his thoughts as follows;
“Perceiving the front and back faces of the cubes become
easier after doing the activities. I solved those questions
faster. At the first activity, I had got more undone
questions, but after the activities the number of undone
questions gradually reduced.”
Tetris game was another activity type applied to students for one week to
enhance their spatial ability. Tetris game is a tool that provides a chance to use
the combination of these skills in a virtual environment and mostly related with
spatial orientation ability. Students were capable of rotating and moving shapes.
The observations indicated that Tetris game attributable to students’ imagining
and rotating ability of geometric shapes in their mind. Since, students were
required to determine the correct empty place not only for the present shape but
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also for the coming shape by rotating it in a given time. Lisi and Wolford (2002)
stated in his study that students’ spatial ability has improved after 11 Tetris game
playing. In addition to this, students were enthusiastic about performing Tetris
activity. Their enthusiasm could effect their motivation so their learning. This
opinion is consistent with the findings of Clements et al. (1997) who stated that
Tetris game motivated and aided students to improve their spatial ability.
When the students’ problem solving methods were examined it was
understood that most of the students used turning in the mind as a problem solving
method in card rotation questions. Tetris and rotation geometry activities were
required to rotate objects in the mind so these activities might help students to
enhance their mental rotation ability. St9 expressed his method for solving card
rotation questions as follows;
“In the beginning, I didn’t know how to handle questions.
However after the activities, I tried to answer the questions
by imagining. I tried to find which shapes would come
after which movement.”
Other problem solving methods were; looking at previous shape, by
controlling symmetry and giving letter to the shapes. Students who used
controlling symmetry method realized that rotation just only changed the
appearance of the shape but symmetry changed the shape itself. They determined
whether the shapes were same by comparing two shapes. St4 explained the
method he used as fallow;
“At first, I tried to rotate shapes in my mind but then, I
gave attention to whether the shapes were symmetrical or
not. I mean, I looked at the initial shape and decided
whether the given shape was symmetrical with the initial
one. I realized that if the shapes were symmetrical they
were not the same.”
Another activity was Architectural-type activity which required drawing
the different point of views of figures and construct figure by looking at top, front
and side views of it. According to my experience the number of students’ correct
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drawing and construction showed increase in the following days of activities. This
pointed to a connection between students’ use of concrete materials and their
performance in orthographic and isometric projection. However, it was more
difficult for students to perform orthographic projection that is representing a
three dimensional (3D) objects in two dimensions (2D) than isometric projection
that is representing a two dimensional (2D) objects in three dimensions (3D).
Students stated that we were responsible to combine three different perspective
views to construct the shape, however drawing the view could be performed just
only look at the constructed shape nothing else. Moreover, this activity was
mostly related with spatial visualization ability because students were required to
manipulate or transform the image of spatial patterns into other arrangements.
A Cuisenaire rod pattern was another activity that was performed by using
concrete materials. The students need to use the rods in solving problems that the
concepts will have concrete foundation. This activity provided valuable spatial
problem solving experience to the students. Although students tried to fill spaces
with randomly selected rods at the beginning, they started to select appropriate
rods to fill given space after a short period of time. In other words students’
method of trial and error turned into the method of implication. As no need to
manipulate parts during the activity, it was mostly related with spatial orientation.
Activities with concrete materials could be the chance of seeing objects instead of
imagines it for students. According to Piaget (1963) spatial ideas progressed at
two different levels which were level of perception (as learned through the sense
of touch and seeing) and level of imagination. Imagination will occur after
completing the level of perception. Students’ imagination ability that is requiring
solving spatial ability problems could be enhanced by means of dealing with
concrete materials.
Students found activities performed by using concrete materials more
enjoyable than activities without them. As these students at the age of 11-12,
games took crucial role in their life, students learnt by playing. The reason for it
could be; they allowed for more creativity and less calculations. This result is
consistent with findings performed by Drickey (2000). According to my
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observations the number of task we performed show increase in the fallowing
days when we compare with first days. In addition to this, the number of mistake
made by students showed decrease in following days. Ben-Haim, Lappan, Houang
(1985) expressed in his study that “concrete experiences with cubes - building,
representing in 2-dimensional drawings, and reading such drawings - are helpful
in improving students' performance” (p.407).
Another reason can be that, transformation geometry activities help students
to imagine shapes in their mind and to learn how to move or rotate objects and
shapes in the given direction and finding symmetry of figures. Students stated in
their interview that transformational geometry activities were helpful in solving
cube comparison and card rotation questions. This result was expected because
solution of these two type questions was depending on imagine and move shapes
in the mind. St. 3 stated that she determined whether the asked shape was same
with given shape in card rotation questions by using symmetry. If the given shape
was symmetric with asked shape, this means that shapes were not same. All
students expect with number 5 expressed that they used imagine in the mind as a
problem solving method after the transformation geometry activities and it assist
them to enhance their imagination ability in the mind. In addition to this % 44 of
students used imagine in the mind, %22 of students used control of symmetry and
% 11 used transform given shape as a problem solving method in cube
comparison test after the transformation geometry activities. These solving
methods were very crucial because they were learnt after transformation geometry
activities. In the study development of students’ spatial thinking in a unit on
geometric motions Clements and Battista (1997) found that flip and turn activity
help students to enhance their mental rotation ability.
Two different types of paper folding activity performed with students;
origami and making shapes. These two types of activities were performed for two
weeks. Origami brings extra meaning to a piece of paper by shaping it into a form
that has symbolism. It is well established among educators that paper folding
could be beneficial as an aid in teaching geometry to children (Geretschlager,
1995). After a short period of time students’ ability to construct shapes,
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understand the terms related geometry, speed of constructing shapes showed
increase in the following days of activities. They could benefit from origami
activities in terms of different features of it. For example, students were required
to listen, understand instruction which includes basic geometry terms such as
edge, face, angel, corner, diagonal, parallel, perpendicular, and bisector and put it
into practice.
All these requirements helped students to enhance their
imagination, construction and guessing ability. Since the shape of paper was
changed into other arrangements after folding, Origami activities were related
with spatial visualization ability. Performing activity related with spatial
visualization was more difficult than activity related with spatial orientation. The
reason for this, spatial visualization requires manipulation or transformation of
spatial patterns’ image into other arrangements. The specific skills involved in the
manifestation of the spatial visualization ability improve with practice (Ben-Haim,
Lappan & Houang, 1988).
Similarly, making shape activities had curious properties such as rotate,
fold, unfold, twist, and fit together in unexpected ways. Activities gave students a
complete nets for all regular stellated polyhedral together with a number of
interesting compounds. Moreover, it gave a chance to enhance their ability to
imagine shapes’ view in their minds after and before folding. %66.6 of students
used folding in the mind, %33.3 of students used guessing, %11.1 of students
used imagination as a problem solving method in paper folding questions.
Students stated in their interview that paper folding activities helped them to solve
paper folding and surface development questions. There were two main points in
paper folding questions. First one was the place of hole and second one was the
number of hole. Students expressed that both place and number were determined
by using ability that was gained from paper folding activities.
It was required to imagine shapes after folding or give a decision about
which folding movement should be done to get given shape in these two activities.
These two activities might help students to enhance their mental folding ability.
According to students’ answer, most of the students used folding in the mind as
problem solving method in paper folding questions. Students used this method to
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find the correct place of the hole. They firstly fold paper in their mind and after
that open this folded paper to find the correct place of the hole. St4 stated his
solving method after the activities as follows;
“While folding the paper, I tried to understand where the
hole could be. I tried to understand the place of hole by
folding and opening shapes in my mind.”
Different than the other test problems, paper fading questions were required
combination of two different abilities. First one was discussed above, finding the
place of the hole. The second ability was to find the number of hole appeared on
the paper after folding. Students used giving attention to number of folding as a
problem solving method. It was good to see that students realized the logarithmic
increase in the hole number with folding number. In other words, students
discovered that if paper folded once, two holes were appeared. If the same paper
folded again, number of hole got twice and so on. However, sts. 7 and 8 had
trouble about finding the exact hole number, although they realized that hole
number increase with folding number.
Since development of spatial ability in neglected in elementary and
secondary school level in our country, it was decided to give great importance to
spatial ability concepts (MEB, 2005). Subjects such as orthographic and isometric
projection, tessellations, transformation geometry, surface area and volume of
prisms were included into new mathematics curriculum. I was their mathematics
teacher so; I was able to examine students’ performance during mathematics
courses which was the part of visual treatment. According to my experience, there
was an increase in students’ understanding of mathematics subjects especially the
subjects that were based on concrete foundation during and after visual treatment
practice so; students could be benefit from mathematics lecture includes spatial
ability concepts. Students stated that it was easier to learn with concrete materials
than just by listening and I observed that students felt confident because of being
familiar to such kind of activities.
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The last interview question was “do you think that time passing between
second and third application period had positive or negative effects on you in
solving third application questions?” The aim of this question was to examine
retention of visual treatment. All students thought that time passing between
second and third application caused a negative affect in solving third application
questions. Most of the students stated that solving third application questions was
more difficult than second application. One of the reasons could be that, since any
visual treatment activity was performed during this period of time, it caused to
forget knowledge that was gained from visual treatment. St3 expressed his
thoughts about retention of visual treatment as follows;
“Solving third application questions was easier than first
application but more difficult than second one. I think that
giving a break to the activities caused to decrease my
spatial knowledge. Therefore, I think that time without any
activity affected me in negative manner.”
These explanations were consistent with inferential finding of this to
research result study. According to research results while students post-test scores
of three tests were higher than pre-test scores, their ret-test scores were lower than
pos-test scores but ret-test score were higher than pre-test scores.
5.1.2. The Discussion of Findings related to feelings toward visual
treatment
According to the results of the interview, most of the students had negative
feelings when they firstly faced spatial ability problems. These feelings were fear,
sadness, tension, anxiety and anger. The reasons for these negative feelings could
be the fact that it was the first time to deal with such kind of questions; that the
procedure couldn’t be understood by the students and not being able to solve
questions. For example, st1 stated the reason for his fear as below;
114
“It was the first time that I faced such kind of questions; I
feared that I wouldn't be able to solve the questions. I had
never met such types of questions before”.
However, 42% of students tend to reflect a “totally agree” perspective
toward spatial ability problems in terms of anxiety after the activities. This result
showed that visual treatment has an effect on anxiety in terms of decreasing it.
Another reason for negative feelings could be the limited time that was
given to complete test. When I examined the results of students’ test scores, I
realized that no one was able to complete whole tests in the first trial. Actually,
this result was expected because it was the first time that students faced with such
kinds of questions and they had question marks in their mind about the solving
method. However, this expected result did not change the reality. St4 stated that;
“I get tensed because I thought that given time to finish test
wouldn't be enough for me.”
While most of the students had negative feelings towards spatial ability
problems, few students had positive feelings. The positive feelings of the students
could be attributed to the characteristics of the activities. For example, Sts. 2 and 4
enjoyed activities even if they didn’t know how to solve questions.
St2 resembled questions to a game and expressed his thought as follows;
“I found questions very interesting. Questions were similar
to a game. While I was solving the questions, I had
difficulty but it's true that I enjoyed myself.”
Another finding can be stated that all students’ feelings were negative when
they could not solve the problem. These feelings were fear, sad, tensed, worry and
nervous. It was understood from the students’ explanations that couldn’t be able
to solve questions was the main reason for the negative feelings. St6 stated his
thoughts as follows;
115
“I found questions very worrying. Because I didn’t know
anything and I hadn't any idea about how questions would
be solved. I got a bit worried while I was solving the
questions.”
St6 tends to reflect a “tend to agree” perspective toward spatial ability
problems in terms of anxiety even after the activities.
In another interview question, students were asked to state their feelings
when their solving method of no avail. Different than the feelings stated in the
first interview question, all students’ feelings were negative in that question.
There was a small difference between first and fourth interview questions. In the
first interview question students were asked to state their feelings before they
started to questions but in the fourth interview question students’ feelings were
asked after they start to solve questions. Students’ feelings were; fear,
demoralization, disappointment, nervousness, angry and panic. Most of the
students thought that they couldn’t be able to solve questions after the failure of
their solving method. The reason for these feelings could be because of not being
able to find alternative problem solving method. It was an expected result
because; students’ spatial knowledge was limited to find an alternative solving
method. As a conclusion, students didn’t find alternative solving method and left
question undone. St7 stated that;
“When I didn’t solve the questions I thought that I
wouldn't able to solve other questions. In addition to this,
given time to solve questions was limited so; I did not
finish solving questions. Therefore I felt nervous.”
Another reason for negative feelings could be the lack of self-confidence
about solving spatial ability problems. Students’ attitude toward spatial ability
problem was getting more positive after visual treatment. Most of the students
stated that they enjoyed during visual treatment.
Students found activities
enjoyable especially performed with manipulative such as pentominoes,
orthographic projection and computer based. The reasons could be stated as;
became familiar with spatial ability problems with activities, understood spatial
116
problem solving strategies, found different solving method for solving questions;
found activities interesting and being the first time that they engaged with such
kind of questions. St4 stated that;
“I found activates very different and enjoyable. I had never
performed such kind of activities .So, when I performed it,
I had a good time.”
Some of the students get bored during the visual treatment. The main reason
for negative feelings was not being able to solve questions. The same students
found Tetris activity funny because they could perform it. St2 stated his opinion
as follows;
“I found activities very boring. I didn’t want to solve the
questions.”
There was a consensus about the usefulness of the activities among students’
opinion. 66% of students stated that activities were helpful in solving spatial
ability questions, 22% of students believed that activities were helpful but limited,
11% of students stated that activities didn’t help him to solve questions. The
reason for usefulness of the activities could be the similarity between problems
asked in tests and activities. Moreover activities provide a chance deal with spatial
ability problems that students didn’t faced with before and also students believed
that activities helped them to solve spatial ability problems faster. St2 thought
different than other students that activity problems were not similar to the test
problems. That is why he thought that benefit of activities was limited. The aim of
the activities was to enhance students’ ability to solve spatial ability problems. St2
may not put the relation between activities and spatial ability problems
The question “what did you gain from the activities” was asked in three
different forms to get clear explanation from students. According to students’
answers to the interview question; sts 1, 2, 4 and 9 believed that activities helped
them to develop spatial thinking ability such as three dimensional thinking ability
and ability to think geometric objects in the mind. Activities were designed to
perform by using spatial ability so this could be the reason for this thought. In
other words, each activity was required different spatial ability such as
117
imagination, transformation and guessing. Results of this study showed that visual
treatment has a positive effect on spatial ability. That is why it was normal for
students to thought as activities helped them to develop spatial thinking ability.
Sts9 tend to reflect an “agree” perspective toward spatial ability problems in terms
of usefulness and expressed his thoughts as follows;
“I was able to put shapes together and imagine shapes in
my mind.”
Other students focused on the sub-dimensional usefulness of the activities
such as creativity, faster problem solving ability, looking problem and situations
from different point of view. These results were not directly related with spatial
abilities. However Just only two students didn’t believe the usefulness of the
activities.
Moreover students were successful in put relation between visual treatment
and daily life usage of spatial gaining. One of the main aims of the study was to
help students to realize the connection between spatial ability and reflection of it
to the daily life.
According to students’ explanations, spatial ability could be
used in; drawing plan of somewhere, attaching mouse to the computer case
without looking it, decorating furniture in the mind before put it into practice,
drawing three dimensional models of cars, preparing a model of house and solving
mathematics questions. St4 gave the example below;
“I believe that, activities are related with our daily life. For
example, we can use our spatial ability to decorate our
furniture in our mind before put it into practice. Activities
enhanced my decoration ability.”
And st5 gave the example below;
“I like drawing car models. I could only two-dimensional
drawings of the car in previous days, but now I can draw
three dimensional appearance of the car.”
These two students tend to reflect an “totally agree” perspective toward
spatial ability problems in terms of usefulness
118
The reason for students to put this relation easily was related with; spatial
ability’s wide spread usage and occupying an important role in our daily life.
Spatial relations were everywhere. Since we are living in a three dimensional
world we are required spatial ability in every field in our life. These activities
provide a chance to students to enhance their awareness about spatial ability and
usefulness of it. When the students’ answers were examined it was understood
that, examples were given from students’ own life
5.2. Implications
In this section recommendations are stated for teachers, curriculum
developers, teacher educators and researchers in order to develop students’ spatial
abilities.
The findings of this research revealed that visual treatment has a potential to
enhance students’ spatial ability. Moreover, students’ attitudes towards spatial
ability problems became more positive after the activities within visual treatment.
In addition to this, this research showed that visual treatment provides students a
chance to examine their thinking processes which they experienced while being
engaged with spatial ability problems.
Teachers:
Based on the findings of this research study and other studies, it can be
suggested that the use of visual treatment will improve students’ spatial ability
(Clements & Owens, 1998; Olkun, 2003; Trindade, 2002). Different kinds of
visual treatment activities that serve the same purpose were applied to students
during the 10-weeks period. This study suggests that teachers will able to reach
students who have different learning potentials and interests by using different
visual treatment activities. And also one of the advantages of the activities is that
their shortcomings can be eliminated by another activity that has not the same
shortcomings. Development of spatial ability can be achieved over a period of
time. That is why teachers should be aware of the importance of spatial ability and
119
make the students be aware of the importance. In addition to this activities were
performed for ten weeks and five days a week. It was suggested that visual
treatment that aims to enhance spatial ability should be applied for a long time
without given any break. Virtual environment and concrete materials are proved
to improve students’ spatial ability (Gabrielli, Rogers & Scaife, 2000; Lisi &
Wolford 2002; Passig & Eden, 2001; Keller, Moses & Hart, 2002; Olkun, Altun
& Smith, 2005) Teachers should perform their activities by using concrete
materials. Another important point that teachers should be careful is the cognitive
level of students. This study was applied with sixth grade elementary level
students and activities were selected with respect to their cognitive level, it is
suggested that selection of the activities should be appropriate with students’
cognitive level. Another suggestion that could be drawn from the study is that
classroom observations and interviews performed with students would provide
beneficial information about students’ feelings and their cognitive process.
Information gathered from interviews will be helpful in preparing activities with
respect to interest and level of students.
Curriculum developers:
Since, the spatial ability is accepted as an important concept for students
both in their academic and work life; it should be handled by curriculum
developers and should be included in text books from elementary level to
university level. Analyze and synthesize of the spatial ability and its dimensions
such as spatial visualization, spatial orientation, spatial perception should be done
and should be adapted to elementary and secondary curriculum. The new
mathematics curriculum has been performed since 2005-2006 academic year in
elementary level but curriculum performed in secondary level is still old. Students
graduate from elementary level will have forgotten the spatial ability knowledge
during secondary education. Because, it was found that the spatial ability scores of
the students decreased after giving a 1 month period without visual treatment in
this research. Curriculum developers should be focused on improves spatial
ability rather than teaching spatial ability by making authors provide concrete
120
activities in textbooks. Moreover, attitude scales should be provided for both
students and teachers to examine their feelings and cognitive process in textbooks.
Teacher educators:
Teacher educators are one of the most important parts in spatial
development process. They are responsible for giving continuation education to
pre-service teachers. In other words teachers’ occupational characteristics get
shape in teacher educators’ hand. That is why teacher educators should have preservice teachers be aware of the importance of spatial ability and should have preservice teachers qualified on how to develop spatial ability.
Recommendation for further studies:
The sample in the study is predominantly elementary middle class families
in a small suburban elementary school. The findings may or may not be applicable
to other situations. Additional research using other elementary schools in other
locations or cities, sample sizes and participants are recommended. In addition to
this study performed with sixth grade elementary school students; research on
students in other grades is clearly called for. The sample population for this study
was small because of using purposive sampling and effect of gender differences
on students’ spatial ability did not examine. In the further research a large
population can be used and effect of gender can be examined. Interviews in the
current research performed with students whose socio-economic level is low so
the students’ ability to express their feelings and thoughts was a bit problematic.
Study with students from different socio-economic level and selecting talkative
students are recommended. Moreover effects of spatial ability on students’
mathematics and geometry achievement can be examined in further researches.
Another important issue that should be handled is the way that teachers use to
introduce and improve spatial ability. Teacher way of introduce spatial ability and
effect of it in improving spatial ability can be examined in further research.
121
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APPENDICES
APPENDIX A
SAMPLE QUESTIONS OF SAT
Paper Folding Test
The square shaped paper on the left side of the vertical line is folded and then a
hole is made. After unfolding the paper, which one of the shapes in the right side
of the vertical line will appear?
Surface Development Test
When the paper is folded from the dotted lines, the subject on the right will be
formed. By imagining the folding of the paper, match the numbered edges to the
letters.
p.c. the surface marked by X on unfolded paper on the left and on the subject on
the right shows the same surfaces.
128
Cube Comparison Test
In the following cubes all the numbers, figures and letters appears onlyonce on
each cube, but it can be in an unseen position. Then, find out whether the cubes on
the left and the right are the same. If the cubes are the same then mark S (Same),
otherwise mark D (Different).
Card Rotation Test
This test requires comparing the shape on the left side of the vertical line with the
eight shapes on the right side of the vertical line. Find out whether the shapes on
the right side can be determined by rotating the shape on the left side of the
129
vertical line, in other words examine whether the shapes are the same or different.
If the shapes are the same as the shape on the left side of the vertical line then
mark S (Same), otherwise mark D (Different).
130
APPENDIX B
INTERVIEW QUESTIONS AND PURPOSE OF THE QUESTIONS
Questions
Purpose(s) of the Questions
What did you feel when you faced with To examine the effects of spatial ability
spatial ability questions for the first questions on students’ feelings
time?
Which solution methods did you use for To investigate the methods that students
solving questions for the first time?
used before taking spatial ability
activities
Did
your
solving
methods
show
changes according to question types in
spatial ability tests?
What did you think about the spatial
ability activities? In generally did you
To investigate whether or not students’
problem solving method show changes
within test types
To investigate students’ feelings about
activities.
got enjoyed or got bored during the
activities?.
Do you think that activities were
beneficial for you to solve spatial
ability questions?
they think about activities, did they put
connection with activities and asked
questions
What did you gained from the activities
was asked to the students?
To got vision of students about what do
To got vision of students about what
kind of achievements did they gain
after 10-activity-week
131
Questions
Purpose(s) of the Questions
Why did you think that spatial ability
activities were so important, do you
To got vision of students about daily
usage of spatial ability activities
think that you will use this information
in your daily life?
Did your problem solving methods
show changes after the activities? I
To got investigate the changes in
methods
mean which problem solving methods
had you used at the first application and
which problem solving method did you
used at the second application?
Which problem solving methods did
you used for card rotation?
To got investigate the changes in
methods used in card rotation questions
and effects of activities on it
Which problem solving methods did
you used for paper folding?
To got investigate the changes in
methods
used
in
paper
folding
questions and effects of activities on it
What kind of method did you follow for
finding number of hole on folding
To investigate the strategy that students
used.
papers?
In which ability you felt change after To investigate change occurred in
spatial activities?
students’ abilities after spatial ability
activities
Which lectures were related with
activities could you please explain it
To understood whether or not students
put connection between spatial ability
with examples?
132
Questions
Purpose(s) of the Questions
In which ability you have feels change
or improvement before and after the
activities in general?
Do you think that the time passing
between second and third application
period had positive or negative effects
on you in solving third application
To understood whether or not students
put connection between spatial ability
activities and lectures
To
have
opinion
about
students
thinking process about the time-break
given to the students for four weeks
after the post-treatment.
questions?
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APPENDIX C
SAMPLE VISUAL TREATMENT ACTIVITY SHEETS
PENTOMINOES ACTIVITY SHEET
Verilen beş kareliler setinden istenenleri kullanarak 3 x 10 Dikdörtgensel
bölgeleri oluşturunuz.
A)
B)
C)
D)
2, 4, 5, 7, 11, 12
1, 2, 3, 4, 5, 11
3, 7, 8, 10, 11, 12
2, 3, 4, 10, 11, 12
[Note: This activity was utilized from the study of Duby (2001, p.8) ]
134
ARCHITECTURAL-TYPE ACTIVITY SHEET
Aşağıda birim küpler kullanılarak oluşturulan yapıların önden, üstten ve yandan
görünüşlerini iki boyutlu olarak çiziniz.
üstten
önden
yandan
üstten
önden
yandan
[Note: This activity was utilized from the study of Davidson & Willcutt (1997,
p.44) ]
135
ROTATION AND REFLECTION ACTIVITY SHEET
Aktivite kâğıdın en üstünde verilen şekli geometrik çubukları kullanarak
oluşturunuz ve şekle uygulanan yansıma ve dönme hareketleri sonrası
görüntüsünü verilen yerlere çiziniz.
[Note: This activity was utilized from the study of Davidson & Willcutt (1997,
p.40) ]
136
SYMMETRY SHADING ACTIVITY SHEET
Aşağıda verilen şekli simetrik olacak şekilde tarayınız.
[Note: This activity was utilized from the study of Kroner (1994, p.54) ]
137
SLIDES, FLIP AND TURN ACTIVITY SHEET
Aşağıdaki şekle uygulanması gereken taşıma geometrisi hareketleri şekillerin
üzerine yazılmıştır. Şeklin hareket sonrası oluşacak görüntüsünü verilen yerlere
örneğe uygun olarak çiziniz.
180 derece döndür.
90 derece döndür.
180 derece döndür.
270 derece döndür.
Dikey simetrisini al.
Yatay simetrisini al.
270 derece döndür.
[Note: This activity was utilized from the study of Kroner (1994, p.14) ]
138
MIRROR PUZZLE ACTIVITY SHEET
Elinizde bulunan aynayı aşağıdaki şekillerin üzerine yerleştirerek referans olarak
verilen şekli elde ediniz ve bulduğunuz yöntemleri gurup arkadaşlarınız ile
tartışınız.
[Note: This activity was utilized from the study of Walter (1996, pp.5-6) ]
139